References
Abergel, F., Anane, M., Chakraborti, A., Jedidi, A., and Toke, I. M. (2016). Limit Order Books. Cambridge University Press.
Abramovich, Y. I. (1981). A controlled method for adaptive optimization of filters using the criterion of maximum signal-to-noise ratio. Engineering and Electronic Physics, 25(3), 87–95.
Ahmadi-Javid, A. (2012). Entropic value-at-risk: A new coherent risk measure. Journal of Optimization Theory and Applications, 155(3), 1105–1123.
Ahmadi-Javid, A., and Fallah-Tafti, M. (2019). Portfolio optimization with entropic value-at-risk. European Journal of Operational Research, 279(1), 225–241.
Ahmed, N. K., Atiya, A. F., Gayar, N. E., and El-Shishiny, H. (2010). An empirical comparison of machine learning models for time series forecasting. Econometric Reviews, 29(5–6), 594–621.
Amos, B., and Kolter, J. Z. (2017). OptNet: Differentiable optimization as a layer in neural networks. In Proceedings of the international conference on machine learning (ICML),Vol. 70, pages 136–145.
Anderson, B. D. O., and Moore, J. B. (1979). Optimal Filtering. Englewood Cliffs: Prentice Hall.
Anderson, R. M., Bianchi, S. W., and Goldberg, L. R. (2012). Will my risk parity strategy outperform? Financial Analysts Journal, 68(6), 75–93.
Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis. Wiley-Interscience.
Ang, A., Chen, J., and Xing, Y. (2006). Downside risk. Review of Financial Studies, 19(4), 1191–1239.
Ardia, D., Bolliger, G., Boudt, K., and Gagnon-Fleury, J.-P. (2017). The impact of covariance misspecification in risk-based portfolios. Annals of Operations Research, 254(1–2), 2–16.
Arnott, R., Harvey, C. R., and Markowitz, H. M. (2019). A backtesting protocol in the era of machine learning. The Journal of Financial Data Science, 1(1), 64–74.
Artzner, P., Delbaen, F., Eber, J. M., and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–227.
Asness, C. S., Frazzini, A., and Pedersen, L. H. (2012). Leverage aversion and risk parity. Financial Analysts Journal, 68(1), 47–59.
Atiya, A. F. (2001). Bankruptcy prediction for credit risk using neural networks: A survey and new results. IEEE Transactions on Neural Networks, 12(4), 929–935.
Avellaneda, M., and Lee, J.-H. (2010). Statistical arbitrage in the US equities market. Quantitative Finance, 10(7), 761–782.
Bacon, C. (2008). Practical Portfolio Performance Measurement and Attribution. John Wiley & Sons.
Bai, X., Scheinberg, K., and Tütüncü, R. (2016). Least-squares approach to risk parity in portfolio selection. Quantitative Finance, 16(3), 357–376.
Bailey, D. H., Borwein, J. M., López de Prado, M., Salehipour, A., and Zhu, Q. J. (2016). Backtest overfitting in financial markets. Automated Trader, 39(2), 52–57.
Bailey, D. H., Borwein, J. M., López de Prado, M., and Zhu, Q. J. (2014). Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance. Notices of the American Mathematical Society, 61(5), 458–471.
Bailey, D. H., Borwein, J. M., López de Prado, M., and Zhu, Q. J. (2017). The probability of backtest overfitting. Journal of Computational Finance (Risk Journals), 20(4), 458–471.
Bailey, D. H., Borwein, J., and López de Prado, M. (2016). Stock portfolio design and backtest overfitting. Journal of Investment Management, 15(1), 1–13.
Bailey, D. H., and López de Prado, M. (2012). The Sharpe ratio efficient frontier. The Journal of Risk, 15(2), 3–44.
Bailey, D. H., and López de Prado, M. (2014). The deflated Sharpe ratio: Correcting for selection bias, backtest overfitting and non-normality. Journal of Portfolio Management, 40(5), 94–107.
Bajalinov, E. B. (2003). Linear-Fractional Programming: Theory, Methods, Applications and Software. Boston: Springer.
Ballings, M., Poel, D. V. den, Hespeels, N., and Gryp, R. (2015). Evaluating multiple classifiers for stock price direction prediction. Expert Systems with Applications, 42(20), 7046–7056.
Banerjee, A., Dolado, J. J., Galbraith, J. W., and Hendry, D. F. (1993). Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data. Oxford University Press.
Banerjee, O., El Ghaoui, L., and d’Aspremont, A. (2008). Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research (JMLR), 9, 485–516.
Barber, B. M., and Odean, T. (2000). Trading is hazardous to your wealth: The common stock investment performance of individual investors. The Journal of Finance, 55(2), 773–806.
Barber, R. F., and Candès, E. J. (2015). Controlling the false discovery rate via knockoffs. The Annals of Statistics, 43(5), 2055–2085.
Bartz, D. (2016). Cross-validation based nonlinear shrinkage. In Proceedings of the 30th annual conference on neural information processing systems (NeurIPS). Barcelona, Spain.
Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95–121.
Beasley, J. E., Meade, N., and Chang, T. J. (2003). An evolutionary heuristic for the index tracking problem. European Journal of Operational Research, 148, 621–643.
Beck, A. (2017). First-Order Methods in Optimization. Society for Industrial and Applied Mathematics (SIAM).
Bender, J., Briand, R., Melas, D., and Subramanian, R. A. (2013). Foundations of factor investing. MSCI Research Insight.
Bengio, Y. (1997). Using a financial training criterion rather than a prediction criterion. International Journal of Neural Systems, 8(4), 433–443.
Bengtsson, M., and Ottersten, B. (2001). Optimal and suboptimal transmit beamforming. In L. C. Godara, editor, Handbook of antennas in wireless communications. Boca Raton, FL: CRC Press.
Benidis, K., Feng, Y., and Palomar, D. P. (2018a). Optimization methods for financial index tracking: From theory to practice. Foundations and Trends in Optimization, Now Publishers, 3(3), 171–279.
Benidis, K., Feng, Y., and Palomar, D. P. (2018b). Sparse portfolios for high-dimensional financial index tracking. IEEE Transactions on Signal Processing, 66(1), 155–170.
Benidis, K., and Palomar, D. P. (2019). sparseIndexTracking: Design of Portfolio of Stocks to Track an Index.
Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 57(1), 289–300.
Ben-Tal, A., El Ghaoui, L., and Nemirovski, A. (2009). Robust Optimization. Princeton University Press.
Ben-Tal, A., and Nemirovski, A. (2001). Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. Society for Industrial and Applied Mathematics (SIAM).
Ben-Tal, A., and Nemirovski, A. (2008). Selected topics in robust convex optimization. Mathematical Programming, 112(1), 125–158.
Bertsekas, D. P. (1999). Nonlinear Programming. Athena Scientific.
Bertsekas, D. P., Nedić, A., and Ozdaglar, A. E. (2003). Convex Analysis and Optimization. Belmont, MA, USA: Athena Scientific.
Bertsekas, D. P., and Tsitsiklis, J. N. (1997). Parallel and Distributed Computation: Numerical Methods. Athena Scientific.
Bertsimas, D., Brown, D. B., and Caramanis, C. (2011). Theory and applications of robust optimization. SIAM Review, 53(3), 464–501.
Best, M. J., and Grauer, R. R. (1991). On the sensitivity of mean–variance-efficient portfolios to changes in asset means: Some analytical and computational results. Review of Financial Studies, 4(2), 315–342.
Birge, J. R., and Louveaux, F. V. (2011). Introduction to Stochastic Programming. Springer.
Birgeand, J., and Chavez-Bedoya, L. (2016). Portfolio optimization under generalized hyperbolic skewed \(t\) distribution and exponential utility. Quantitative Finance, 16(7), 1019–1036.
Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
Black, F., and Litterman, R. (1991). Asset allocation: Combining investor views with market equilibrium. The Journal of Fixed Income, 2(1), 7–18.
Bogdanov, A., Mossel, E., and Vadhan, S. (2008). The complexity of distinguishing Markov random fields. In Approximation, randomization and combinatorial optimization. Algorithms and techniques, pages 331–342. Springer.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. The Review of Economics and Statistics, 3(72), 498–505.
Bollerslev, T., Chou, R. Y., and Kroner, K. F. (1992). ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics, 52, 5–59.
Bontempi, G., Taieb, S. B., and Borgne, Y.-A. L. (2012). Machine learning strategies for time series forecasting. In M.-A. Aufaure and E. Zimányi, editors, Business intelligence, pages 62–77. Springer.
Bouchaud, J.-P., Bonart, J., Donier, J., and Gould, M. (2018). Trades, Quotes and Prices: Financial Markets Under the Microscope. Cambridge University Press.
Boudt, K., Cornilly, D., Holle, F. V., and Willems, J. (2020). Algorithmic portfolio tilting to harvest higher moment gains. Heliyon, 6(3), e03516.
Boudt, K., Cornilly, D., and Verdonck, T. (2020). A coskewness shrinkage approach for estimating the skewness of linear combinations of random variables. Journal of Financial Econometrics, 18(1), 1–23.
Boudt, K., Lu, W., and Peeters, B. (2014). Higher order comoments of multifactor models and asset allocation. Finance Research Letters, 13, 225–233.
Box, G. E., and Pierce, D. A. (1970). Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65(332), 1509–1526.
Box, G. E., and Tiao, G. C. (1977). A canonical analysis of multiple time series. Biometrika, 64(2), 355–365.
Boyd, S., Busseti, E., Diamond, S., Kahn, R., Koh, K., Nystrup, P., and Speth, J. (2017). Multi-period trading via convex optimization. Foundations and Trends in Optimization, Now Publishers, 3(1), 1–76.
Boyd, S., Kim, S. J., Vandenberghe, L., and Hassibi, A. (2007). A Tutorial on Geometric Programming. Springer.
Boyd, S., Parikh, N., Chu, E., Peleato, B., and Eckstein, J. (2010). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, Now Publishers, 3(1), 1–122.
Boyd, S., and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
Brandt, M. W., Santa-Clara, P., and Valkanov, R. (2009). Parametric portfolio policies: Exploiting characteristics in the cross section of equity returns. Review of Financial Studies, 22(9), 3411–3447.
Breiman, L. (1996). Bagging predictors. Machine Learning, 24, 123–140.
Breiman, L. (2001). Statistical modelling: The two cultures. Statistical Science, 16(3), 199–231.
Briec, W., Kerstens, K., and Jokung, O. (2007). Mean–variance–skewness portfolio performance gauging: A general shortage function and dual approach. Management Science, 53(1), 135–149.
Brockwell, P. J., and Davis, R. A. (2002). Introduction to Time Series and Forecasting. Springer.
Bruder, B., and Roncalli, T. (2012). Managing risk exposures using the risk budgeting approach. MPRA Paper 37246.
Bubeck, S., Chandrasekaran, V., Eldan, R., Gehrke, J., Horvitz, E., Kamar, E., … Zhang, Y. (2023). Sparks of artificial general intelligence: Early experiments with GPT-4. Preprint. Available at arXiv.
Bun, J., Bouchaud, J.-P., and Potters, M. (2006). Cleaning correlation matrices. Risk Magazine.
Bun, J., Bouchaud, J.-P., and Potters, M. (2017). Cleaning large correlation matrices: Tools from random matrix theory. Physics Reports, 666, 1–109.
Butler, A., and Kwon, R. H. (2023). Integrating prediction in mean–variance portfolio optimization. Quantitative Finance, 23(3), 429–452.
Cajas, Dany. (2021a). Entropic portfolio optimization: A disciplined convex programming framework. SSRN Electronic Journal.
Cajas, Dany. (2021b). Kelly portfolio optimization: A disciplined convex programming framework. SSRN Electronic Journal.
Cajas, D. (2023). Riskfolio-Lib.
Campbell, J. Y., Lo, A. W., and MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton, NJ: Princeton University Press.
Candès, E. J., and Tao, T. (2005). Decoding by linear programming. IEEE Transactions on Information Theory, 51(12), 4203–4215.
Candès, E. J., Wakin, M. B., and Boyd, S. P. (2008). Enhancing sparsity by reweighted \(\ell_1\) minimization. Journal of Fourier Analysis and Applications, 14, 877–905.
Cao, L. J., and Tay, F. E. H. (2003). Support vector machine with adaptive parameters in financial time series forecasting. IEEE Transactions on Neural Networks, 14(6), 1506–1518.
Cardoso, J. V. M., and Palomar, D. P. (2020). Learning undirected graphs in financial markets. In Proceedings of the 54th asilomar conference on signals, systems and computers, pages 741–745. Pacific Grove, CA, USA: IEEE.
Cardoso, J. V. M., and Palomar, D. P. (2021). riskParityPortfolio: Design of Risk Parity Portfolios.
Cardoso, J. V. M., and Palomar, D. P. (2022). spectralGraphTopology: Learning Graphs from Data via Spectral Constraints.
Cardoso, J. V. M., and Palomar, D. P. (2023a). finbipartite: Learning Bipartite Graphs: Heavy Tails and Multiple Components.
Cardoso, J. V. M., and Palomar, D. P. (2023b). fingraph: Learning Graphs for Financial Markets.
Cardoso, J. V. M., Ying, J., and Palomar, D. P. (2021). Graphical models in heavy-tailed markets. In Proceedings of 35th international conference on neural information processing systems (NeurIPS), pages 19989–20001. Virtual: Curran Associates Inc.
Cardoso, J. V. M., Ying, J., and Palomar, D. P. (2022a). Learning bipartite graphs: Heavy tails and multiple components. In Proceedings of the 36th international conference on neural information processing systems (NeurIPS), pages 14044–14057. New Orleans, LA, USA: Curran Associates Inc.
Cardoso, J. V. M., Ying, J., and Palomar, D. P. (2022b). Nonconvex graph learning: Sparsity, heavy-tails, and clustering. In P. Diniz, editor, Signal processing and machine learning theory, pages 1049–1072. Elsevier.
Chan, E. P. (2008). Quantitative Trading: How to Build Your Own Algorithmic Trading Business. John Wiley & Sons.
Chan, E. P. (2013). Algorithmic Trading: Winning Strategies and Their Rationale. John Wiley & Sons.
Chares, R. (2007). Cones and Interior-Point Algorithms for Structured Convex Optimization Involving Powers and Exponentials (PhD thesis). Université Catholique de Louvain; École Polytechnique de Louvain.
Charnes, A., and Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3–4), 181–186.
Chassein, A., and Goerigk, M. (2015). Alternative formulations for the ordered weighted averaging objective. Information Processing Letters, 115, 604–608.
Chaves, D. B., Hsu, J. C., Li, F., and Shakernia, O. (2011). Risk parity portfolio vs. Other asset allocation heuristic portfolios. Journal of Investing, 20(1), 108–118.
Chaves, D. B., Hsu, J. C., Li, F., and Shakernia, O. (2012). Efficient algorithms for computing risk parity portfolio weights. Journal of Investing, 21(3), 150–163.
Chekhlov, A., Uryasev, S., and Zabarankin, M. (2004). Portfolio optimization with drawdown constraints. In P. M. Pardalos, A. Migdalas, and G. Baourakis, editors, Supply chain and finance, pages 209–228. World Scientific.
Chekhlov, A., Uryasev, S., and Zabarankin, M. (2005). Drawdown measure in portfolio optimization. International Journal of Theoretical and Applied Finance, 8(1), 13–58.
Chen, R., Y. Feng, and Palomar, D. P. (2016). Forecasting intraday trading volume: A Kalman filter approach. SSRN Electronic Journal.
Chen, Y., Wiesel, A., and Hero III, A. O. (2011). Robust shrinkage estimation of high-dimensional covariance matrices. IEEE Transactions on Signal Processing, 59(9), 4097–4107.
Chiang, M. (2005). Geometric programming for communication systems. Foundations and Trends in Communications and Information Theory, 2(1–2), 1–154.
Choi, J., and Chen, R. (2022). Improved iterative methods for solving risk parity portfolio. Journal of Derivatives and Quantitative Studies, 30(2), 114–124.
Chopra, V., and Ziemba, W. (1993). The effect of errors in means, variances and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2), 6–11.
Choueifaty, Y., and Coignard, Y. (2008). Toward maximum diversification. Journal of Portfolio Management, 35, 40–51.
Christoffersen, P., Errunza, V., Jacobs, K., and Langlois, H. (2012). Is the potential for international diversification disappearing? A dynamic copula approach. The Review of Financial Studies, 25, 3711–3751.
Chung, F. R. K. (1997). Spectral Graph Theory. Providence: American Mathematical Society.
Clegg, M. (2014). On the persistence of cointegration in pairs trading. SSRN Electronic Journal.
Clegg, M. (2023). egcm: Engle–Granger Cointegration Models.
Clegg, M., and Krauss, C. (2018). Pairs trading with partial cointegration. Quantitative Finance, 18(1), 121–138.
Cont, R. (2001). Empirical properties of assets returns: Stylised facts and statistical issues. Quantitative Finance, 1, 223–236.
Cornuejols, G., and Tütüncü, R. (2006). Optimization Methods in Finance. Cambridge University Press.
Cotton, P. (2023). Schur Complementary Portfolios – a Unification of Machine Learning and Optimization-Based Portfolio Construction.
Cover, T., and Thomas, J. (1991). Elements of Information Theory. John Wiley & Sons.
Cowpertwait, P. S. P., and Metcalfe, A. V. (2009). Introductory Time Series with R. Springer.
Cuturi, M., and d’Aspremont, A. (2013). Mean reversion with a variance threshold. In Proceedings of the international conference on machine learning (ICML),Vol. 28, pages 271–279.
Cuturi, M., and d’Aspremont, A. (2016). Mean-reverting portfolios: Tradeoffs between sparsity and volatility. In A. N. Akansu, S. R. Kulkarni, and D. M. Malioutov, editors, Financial signal processing and machine learning, pages 23–40. John Wiley & Sons.
Cvitanic, J., and Karatzas, I. (1995). On portfolio optimization under “drawdown” constraints. IMA Lecture Notes in Mathematics & Applications, 65, 77–88.
d’Aspremont, A. (2011). Identifying small mean-reverting portfolios. Quantitative Finance, 11(3), 351–364.
Daubechies, I., Devore, R., Fornasier, M., and Güntürk, C. S. N. (2010). Iteratively reweighted least squares minimization for sparse recovery. Communications on Pure and Applied Mathematics, 63, 1–38.
DeMiguel, V., Garlappi, L., Nogales, F. J., and Uppal, R. (2009). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Science, 55(5), 798–812.
DeMiguel, V., Garlappi, L., and Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22(5), 1915–1953.
Dempster, A. P. (1972). Covariance selection. Biometrics, 28(1), 157–175.
Dickey, D. A., and Fuller, W. A. (1979). Distribution of the estimators for autore-gressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.
Ding, Z., and Granger, C. W. J. (1996). Modeling volatility persistence of speculative returns: A new approach. Journal of Econometrics, 73(1), 185–215.
Dinh, T. P., and Niu, Y.-S. (2011). An efficient DC programming approach for portfolio decision with higher moments. Computational Optimization and Applications, 50(3), 525–554.
Dinkelbach, W. (1967). On nonlinear fractional programming. Management Science, 133(7), 492–498.
Dixon, M. F., Halperin, I., and Bilokon, P. (2020). Machine Learning in Finance. Springer.
Dong, X., Thanou, D., Frossard, P., and Vandergheynst, P. (2015). Laplacian matrix learning for smooth graph signal representation. In Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), pages 3736–3740. Brisbane, Australia.
Dong, X., Thanou, D., Rabbat, M., and Frossard, P. (2019). Learning graphs from data: A signal representation perspective. IEEE Signal Processing Magazine, 36(3), 44–63.
Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.
Dose, C., and Cincotti, S. (2005). Clustering of financial time series with application to index and enhanced index tracking portfolio. Physica A: Statistical Mechanics and Its Applications, 355(1), 145–151.
Duchin, R., and Levy, H. (2009). Markowitz versus the Talmudic portfolio diversification strategies. Journal of Portfolio Management, 35(2), 71.
Durbin, J., and Koopman, S. J. (2012). Time Series Analysis by State Space Methods. Oxford University Press.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26.
Efron, B., and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Springer.
Egilmez, H. E., Pavez, E., and Ortega, A. (2017). Graph learning from data under Laplacian and structural constraints. IEEE Journal of Selected Topics in Signal Processing, 11(6), 825–841.
Ehrman, D. S. (2006). The Handbook of Pairs Trading: Strategies Using Equities, Options, and Futures. John Wiley & Sons.
El Ghaoui, L., Oks, M., and Oustry, F. (2003). Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Operations Research, 51(4), 543–556.
Elad, M. (2010). Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer.
Elliott, R. J., Van Der Hoek, J., and Malcolm, W. P. (2005). Pairs trading. Quantitative Finance, 5(3), 271–276.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 50(4), 987–1007.
Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350.
Engle, R. F., and Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society, 55(2), 251–276.
Engle, R. F., and Sokalska, M. E. (2012). Forecasting intraday volatility in the US equity market. Multiplicative component GARCH. Journal of Financial Econometrics, 10(1), 54–83.
Esling, P., and Agon, C. (2012). Time series data mining. ACM Computing Surveys, 45(1), 1–34.
Estrada, J. (2006). Downside risk in practice. Journal of Applied Corporate Finance, 18(1), 117–125.
Estrada, J. (2008). Mean–semivariance optimization: A heuristic approach. Journal of Applied Finance, 18(1), 57–72.
Fabozzi, F. J., Focardi, S. M., and Kolm, P. N. (2010). Quantitative Equity Investing: Techniques and Strategies. John Wiley & Sons.
Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., and Focardi, S. M. (2007). Robust Portfolio Optimization and Management. John Wiley & Sons.
Fama, E. F. (1965). The behavior of stock-market prices. The Journal of Business, 38(1), 34–105.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.
Fama, E. F., and French, K. R. (1992). The cross-section of expected stock returns. The Journal of Finance, 47(2), 427–465.
Fama, E. F., and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.
Fama, E. F., and French, K. R. (2015). A five-factor asset pricing model. The Journal of Finance, 116(1), 1–22.
Fan, K. (1949). On a theorem of Weyl concerning eigenvalues of linear transformations I. Proceedings of the National Academy of Sciences of the United States of America, 35(11), 652.
Feng, Y., and Palomar, D. P. (2015). SCRIP: Successive convex optimization methods for risk parity portfolios design. IEEE Transactions on Signal Processing, 63(19), 5285–5300.
Feng, Y., and Palomar, D. P. (2016). A signal processing perspective on financial engineering. Foundations and Trends in Signal Processing, Now Publishers, 9(1–2), 1–231.
Fischer, T., and Krauss, C. (2018). Deep learning with long short-term memory networks for financial market predictions. European Journal of Operational Research, 270(2), 654–669.
Fishburn, P. C. (1977). Mean-risk analysis with risk associated with below-target returns. American Economic Review, 67(2), 116–126.
Friedman, J., Hastie, T., and Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432–441.
Fu, A., Narasimhan, B., and Boyd, S. (2020). CVXR: An R package for disciplined convex optimization. Journal of Statistical Software, 94(14), 1–34.
Fu, A., Narasimhan, B., Kang, D. W., Diamond, S., Miller, J., Boyd, S., and Rosenfield, P. K. (2022). CVXR: Disciplined Convex Optimization.
Gatev, E., Goetzmann, W. N., and Rouwenhorst, K. G. (2006). Pairs trading: Performance of a relative-value arbitrage rule. Review of Financial Studies, 19(3), 797–827.
Ghalanos, A. (2022). rugarch: Univariate GARCH Models.
Glabadanidis, P. (2015). Market timing with moving averages. International Review of Finance, 15(3), 387–425.
Goetzmann, W. N., and Kumar, A. (2008). Equity portfolio diversification. Review of Finance, 12(3), 433–463.
Goldfarb, D., and Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28(1), 1–38.
Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning. MIT Press.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., … Bengio, Y. (2014). Generative adversarial nets. In Proceedings of the 27th international conference on neural information processing systems (NeurIPS),Vol. 27, pages 2672–2680.
Grant, M., and Boyd, S. (2008). Graph implementations for nonsmooth convex programs. In V. Blondel, S. Boyd, and H. Kimura, editors, Recent advances in learning and control, pages 95–110. Springer.
Grant, M., and Boyd, S. (2014). CVX: Matlab Software for Disciplined Convex Programming.
Grinblatt, M., Titman, S., and Wermers, R. (1995). Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior. American Economic Review, 85, 1088–1105.
Grinold, R. C., and Kahn, R. N. (2000). Active Portfolio Management. McGraw Hill.
Grippo, L., and Sciandrone, M. (2000). On the convergence of the block nonlinear Gauss–Seidel method under convex constraints. Operations Research Letters, 26(3), 127–136.
Griveau-Billion, T., Richard, J.-C., and Roncalli, T. (2013). A fast algorithm for computing high-dimensional risk parity portfolios. SSRN Electronic Journal.
Grootveld, H., and Hallerbach, W. (1999). Variance vs downside risk: Is there really that much difference? European Journal of Operational Research, 114, 304–319.
Grossman, S. J., and Zhou, Z. (1993). Optimal investment strategies for controlling drawdowns. Mathematical Finance, 3(3), 241–276.
Hallerbach, W. G. (2003). Decomposing portfolio value-at-risk: A general analysis. Journal of Risk, 5(2), 1–18.
Harris, R. I. D. (1995). Using Cointegration Analysis in Econometric Modelling. Prentice Hall.
Harvey, A. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.
Harvey, A., and Koopman, S. J. (2009). Unobserved components models in economics and finance: The role of the Kalman filter in time series econometrics. IEEE Control Systems Magazine, 29(6), 71–81.
Harvey, A., Ruiz, E., and Shephard, N. (1994). Multivariate stochastic variance models. The Review of Economic Studies, 61(2), 247–264.
Harvey, C. R. (2017). Presidential address: The scientific outlook in financial economics. The Journal of Finance, 72(4), 1399–1440.
Harvey, C. R., Liu, Y., and Zhu, H. (2016)... And the cross-section of expected returns. Review of Financial Studies, 29(1), 5–68.
Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning. Springer.
Helske, J. (2017). KFAS: Exponential family state space models in R. Journal of Statistical Software, 78(10), 1–39.
Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion probabilistic models. In Proceedings of the 34th international conference on neural information processing systems (NeurIPS), pages 6840–6851. Virtual.
Ho, T. K. (1998). The random subspace method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 832–844.
Hochreiter, S., and Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.
Holmes, E. E., Ward, E. J., and Wills, K. (2012). MARSS: Multivariate autoregressive state-space models for analyzing time-series data. The R Journal, 4(1), 11–19.
Hong, L. J., Hu, Z., and Liu, G. (2014). Monte Carlo methods for value-at-risk and conditional value-at-risk: A review. ACM Transactions on Modeling and Computer Simulation, 24(4), 1–37.
Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 52(1), 105–124.
Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Statistics, 53(1), 73–101.
Huber, P. J. (2011). Robust Statistics. Springer.
Hunter, D. R., and Lange, K. (2004). A tutorial on MM algorithms. The American Statistician, 58, 30–37.
Hyndman, R. J., Koehler, A. B., Ord, J. K., and Snyder, R. D. (2008). Forecasting with Exponential Smoothing. Springer.
Jacobs, B. I., Levy, K. N., and Markowitz, H. M. (2005). Portfolio optimization with factors, scenarios, and realistic short positions. Operations Research, 53(4), 586–599.
Jagannathan, R., and Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance, 58(4), 1651–1684.
James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013). An Introduction to Statistical Learning: With Applications in R. Springer.
James, W., and Stein, C. (1961). Estimation with quadratic loss. In Proceedings of the 4th berkeley symposium on mathematical statistics and probability,Vol. Vol. 1, pages (pp. 361–379). University of California Press.
Jansen, R., and Van Dijk, R. (2002). Optimal benchmark tracking with small portfolios. Journal of Portfolio Management, 28(2), 33–39.
Jean, W. H. (1971). The extension of portfolio analysis to three or more parameters. Journal of Financial and Quantitative Analysis, 6(1), 505–515.
Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 59(6), 1551–1580.
Johansen, S. (1995). Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.
Jolliffe, I. (2002). Principal Component Analysis. Springer.
Jondeau, E., Poon, S. H., and Rockinger, M. (2007). Financial Modeling Under Non-Gaussian Distributions. Springer.
Jorion, P. (1986). Bayes–Stein estimation for portfolio analysis. Journal of Finance and Quantitative Analysis, 21(3), 279–292.
Jorion, P. (1992). Portfolio optimization in practice. Financial Analysts Journal, 48(1), 68–74.
Jurczenko, E. (2017). Factor Investing: From Traditional to Alternative Risk Premia. Amsterdam, The Netherlands: Elsevier.
Jurczenko, E., Maillet, B., and Merlin, P. (2006). Hedge fund portfolio selection with higher-order moments: A nonparametric mean–variance–skewness–kurtosis efficient frontier. In E. Jurczenko and B. Maillet, editors, Multi-moment asset allocation and pricing models, pages 51–66. John Wiley & Sons.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82, 35–45.
Kalofolias, V. (2016). How to learn a graph from smooth signals. In Proceedings of the international conference on artificial intelligence and statistics (AISTATS), pages 920–929.
Kalofolias, V., Loukas, A., Thanou, D., and Frossard, P. (2017). Learning time varying graphs. In Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), pages 2826–2830. New Orleans, LA, USA.
Karmarkar, N. (1984). A new polynomial time algorithm for linear programming. Combinatorica, 4(4), 373–395.
Kastner, G. (2016). Dealing with stochastic volatility in time series using the R package stochvol. Journal of Statistical Software, 69(5), 1–30.
Kay, S. M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall.
Kaya, H., and Lee, W. (2012). Demystifying risk parity. SSRN Electronic Journal.
Kedem, B. (1994). Time Series Analysis by Higher Order Crossings. IEEE Press.
Kelly, Jr., J. L. (1956). A new interpretation of information rate. The Bell System Technical Journal, 35(4), 917–926.
Kent, J. T., and Tyler, D. E. (1991). Redescending \(M\)-estimates of multivariate location and scatter. The Annals of Statistics, 19(4), 2102–2119.
Kent, J. T., Tyler, D. E., and Vard, Y. (1994). A curious likelihood identity for the multivariate \(t\)-distribution. Communications in Statistics – Simulation and Computation, 23(2), 441–453.
Khamaru, K., and Mazumder, R. (2019). Computation of the maximum likelihood estimator in low-rank factor analysis. Mathematical Programming, 176, 279–310.
Kim, S., Shephard, N., and Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies, 65, 361–393.
Kissell, R. (2020). Algorithmic Trading Methods: Applications Using Advanced Statistics, Optimization, and Machine Learning Techniques. Academic Press.
Kleiner, A., Talwalkar, A., Sarkar, P., and Jordan, M. I. (2014). A scalable bootstrap for massive data. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 76(4), 795–816.
Kolaczyk, E. D. (2009). Statistical Analysis of Network Data: Methods and Models. New York: Springer.
Kolm, P. N., Tütüncü, R., and Fabozzi, F. J. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371.
Kramer, M. A. (1991). Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal, 37(2), 233–243.
Krauss, C. (2017). Statistical arbitrage pairs trading strategies: Review and outlook. Journal of Economic Surveys, 31(2), 513–545.
Kritzman, M., Page, S., and Turkington, D. (2010). In defense of optimization: The fallacy of 1/N. Financial Analysts Journal, 66(2), 31–39.
Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012). ImageNet classification with deep convolutional neural networks. In Proceedings of the 25th international conference on neural information processing systems (NeurIPS),Vol. 25, pages 1097–1105.
Kumar, S., Ying, J., Cardoso, J. V. M., and Palomar, D. P. (2019). Structured graph learning via Laplacian spectral constraints. In Proceedings of the 33rd international conference on neural information processing systems (NeurIPS), pages 11651–11663. Vancouver, Canada: Curran Associates Inc.
Kumar, S., Ying, J., Cardoso, J. V. M., and Palomar, D. P. (2020). A unified framework for structured graph learning via spectral constraints. Journal of Machine Learning Research (JMLR), 21(22), 1–60.
Lahiri, S. N. (1999). Theoretical comparisons of block bootstrap methods. The Annals of Statistics, 27(1), 386–404.
Lai, T.-Y. (1991). Portfolio selection with skewness: A multiple- objective approach. Review of Quantitative Finance and Accounting, 1(3), 293–305.
Lake, B., and Tenenbaum, J. (2010). Discovering structure by learning sparse graphs. In Proceedings of the 32nd annual conference of the cognitive science society, pages 778–783.
Lauritzen, S. (1996). Graphical Models. Oxford: Oxford University Press.
LeCun, Y., Bengio, Y., and Hinton, G. (2015). Deep learning. Nature, 521, 436–444.
LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. (1998). Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11), 2278–2324.
Ledoit, O., and Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603–621.
Ledoit, O., and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365–411.
Ledoit, O., and Wolf, M. (2017). Nonlinear shrinkage of the covariance matrix for portfolio selection. The Review of Financial Studies, 30(12), 4349–4388.
Lehalle, C.-A., and Laruelle, S. (Eds.). (2018). Market Microstructure in Practice. World Scientific Publishing Co. Pte. Ltd.
Levy, H., and Markowitz, H. M. (1979). Approximating expected utility by a function of mean and variance. The American Economic Review, 69(3), 308–317.
Lin, H. W., Tegmark, M., and Rolnick, D. (2017). Why does deep and cheap learning work so well? Journal of Statistical Physics, 168, 1223–1247.
Litterman, R. (1996). Hot spots and hedges. Journal of Portfolio Management, 22, 52–75.
Liu, C., and Rubin, D. B. (1995). ML estimation of the \(t\)-distribution using EM and its extensions, ECM and ECME. Statistica Sinica, 5(1), 19–39.
Liu, C., Rubin, D. B., and Wu, Y. N. (1998). Parameter expansion to accelerate EM: The PX-EM algorithm. Biometrika, 85(4), 755–770.
Lo, A. W., and Mackinlay, A. C. (2002). A Non-Random Walk down Wall Street. Princeton, NJ: Princeton University Press.
Lobo, M. S. (2000). Robust and Convex Optimization with Applications in Finance (PhD thesis). Stanford University.
Lobo, M. S., Vandenberghe, L., Boyd, S., and Lebret, H. (1998). Applications of second-order cone programming. Linear Algebra and Applications, 284(1–3), 193–228.
Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD conference. Taipei, Taiwan.
López de Prado, M. (2016). Building diversified portfolios that outperform out of sample. Journal of Portfolio Management, 42(4), 59–69.
López de Prado, M. (2018a). Advances in Financial Machine Learning. John Wiley & Sons.
López de Prado, M. (2018b). The 10 reasons most machine learning funds fail. Journal of Portfolio Management, 44(6), 120–133.
López de Prado, M. (2019). Ten applications of financial machine learning. SSRN Electronic Journal.
Luenberger, D. G. (1969). Optimization by Vector Space Methods. New York: John Wiley & Sons.
Luenberger, D. G., and Ye, Y. (2021). Linear and Nonlinear Programming. Springer.
Luo, Y., Alvarez, M., Wang, S., Jussa, J., Wang, A., and Rohal, G. (2014). Seven sins of quantitative investing. White Paper, Deutsche Bank Markets Research.
Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer.
Machkour, J., Muma, M., and Palomar, D. P. (2025). The terminating-random experiments selector: Fast high-dimensional variable selection with false discovery rate control. Signal Processing.
Machkour, J., Palomar, D. P., and Muma, M. (2024). FDR-controlled portfolio optimization for sparse financial index tracking. Available at arXiv.
Machkour, J., Tien, S., Palomar, D. P., and Muma, M. (2024). TRexSelector: T-Rex Selector: High-Dimensional Variable Selection & FDR Control.
MacLean, L., Thorp, E., and Ziemba, W. (2010). Long-term capital growth: The good and bad properties of the Kelly and fractional Kelly capital growth criteria. Quantitative Finance, 10(7), 681–687.
Maillard, S., Roncalli, T., and Teiletche, J. (2010). The properties of equally weighted risk contribution portfolios. Journal of Portfolio Management, 36(4), 60–70.
Malkiel, B. G. (1973). A Random Walk down Wall Street. New York: W. W. Norton.
Mandelbrot, B. B. (1963). The variation of certain speculative prices. The Journal of Business, 36(4), 394–419.
Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B – Condensed Matter and Complex Systems, 11, 193–197.
Maringer, D., and Oyewumi, O. (2007). Index tracking with constrained portfolios. Intelligent Systems in Accounting, Finance and Management, 15(1–2), 57–71.
Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons.
Markowitz, H. M. (2014). Mean–variance approximations to expected utility. European Journal of Operational Research, 234(2), 346–355.
Maronna, R. A. (1976). Robust \(M\)-estimators of multivariate location and scatter. The Annals of Statistics, 4(1), 51–67.
Maronna, R. A., Martin, D. R., and Yohai, V. J. (2006). Robust Statistics: Theory and Methods. John Wiley & Sons.
Martellini, L., and Ziemann, V. (2010). Improved estimates of higher-order comoments and implications for portfolio selection. The Review of Financial Studies, 23(4), 1467–1502.
Marti, G., Nielsen, F., Binkowski, M., and Donnat, P. (2021). A review of two decades of correlations, hierarchies, networks and clustering in financial markets. In F. Nielsen, editor, Progress in information geometry, pages 245–274. Springer.
Martin, R. A. (2021). PyPortfolioOpt: Portfolio optimization in Python. Journal of Open Source Software, 6(61), 1–5.
Mateos, G., Segarra, S., Marques, A. G., and Ribeiro, A. (2019). Connecting the dots. IEEE Signal Processing Magazine, 36(3), 16–43.
Mausser, H., and Romanko, O. (2014). Computing equal risk contribution portfolios. Journal of Research and Development, 58(4), 5:1–5:12.
Mayer, J., Khairy, K., and Howard, J. (2010). Drawing an elephant with four complex parameters. American Journal of Physics, 78(6), 648–649.
McNeil, A. J., and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. Journal of Empirical Finance, 7(3–4), 271–300.
McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management. Princeton University Press.
Meinshausen, N. (2013). Sign-constrained least squares estimation for high-dimensional regression. Electronic Journal of Statistics, 7, 1607–1631.
Meucci, A. (2005). Risk and Asset Allocation. Springer.
Michaud, R. O. (1989). The Markowitz optimization enigma: Is “optimized” optimal? Financial Analysts Journal, 45(1), 31–42.
Michaud, R. O., and Michaud, R. O. (1998). Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation. Harvard Business School Press.
Michaud, R. O., and Michaud, R. O. (2007). Estimation error and portfolio optimization: A resampling solution. Journal of Investment and Management, 6(1), 8–28.
Michaud, R. O., and Michaud, R. O. (2008). Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation. Oxford University Press.
Montier, J. (2005). Seven sins of fund management. Dresdner Kleinwort Wasserstein – Global Equity Strategy.
Nadarajah, S., Zhang, B., and Chan, S. (2014). Estimation methods for expected shortfall. Quantitative Finance, 14(2), 271–291.
Nemirovski, A. (2000). Lectures on Modern Convex Optimization. Technion - Israel Institute of Technology.
Nesterov, Y. (2018). Lectures on Convex Optimization. Springer.
Nesterov, Y., and Nemirovski, A. (1994). Interior-Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
Neumann, J. von, and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
Nie, F., Wang, X., Jordan, M., and Huang, H. (2016). The constrained Laplacian rank algorithm for graph-based clustering. In Proceedings of the AAAI conference on artificial intelligence, pages 1969–1976. Phoenix, Arizona, USA.
Nielsen, M. A. (2015). Neural Networks and Deep Learning. Determination Press. Available online.
Niu, Y.-S., and Wang, Y.-J. (2019). Higher-order moment portfolio optimization via the difference-of-convex programming and sums-of-squares. Preprint. Available at arXiv.
Nocedal, J., and Wright, S. J. (2006). Numerical Optimization. Springer.
Ogryczak, W. (2000). Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97, 143–162.
Ogryczak, W., and Sliwinski, T. (2003). On solving linear programs with the ordered weighted averaging objective. European Journal of Operational Research, 148, 80–91.
Oja, H. (2013). Multivariate median. In C. Becker, R. Fried, and S. Kuhnt, editors, Robustness and complex data structures. Berlin, Germany: Springer.
Ollila, E., Palomar, D. P., and Pascal, F. (2023). Affine equivariant Tyler’s M-estimator applied to tail parameter learning of elliptical distributions. IEEE Signal Processing Letters, 30, 1017–1021.
Ollila, E., Pascal, F., and Palomar, D. P. (2021). Shrinking the eigenvalues of M-estimators of covariance matrix. IEEE Transactions on Signal Processing, 69, 256–269.
Ollila, E., and Raninen, E. (2019). Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions. IEEE Transactions on Signal Processing, 67(10), 2707–2719.
OpenAI. (2023). GPT-4 technical report. Preprint. Available at arXiv.
Ozbayoglu, A. M., Gudelek, M. U., and Sezer, O. B. (2020). Deep learning for financial applications: A survey. Preprint. Available at arXiv.
Palomar, D. P., and Eldar, Y. C. (2009). Convex Optimization in Signal Processing and Communications. Cambridge University Press.
Palomar, D. P., Zhou, R., Wang, X., Pascal, F., and Ollila, E. (2023). fitHeavyTail: Mean and Covariance Matrix Estimation Under Heavy Tails.
Papenbrock, J. (2011). Asset Clusters and Asset Networks in Financial Risk Management and Portfolio Optimization (PhD thesis). Karlsruher Institute für Technologie.
Papoulis, A. (1991). Probability, Random Variables, and Stochastic Processes. McGraw-Hill.
Pardo, R. (2008). The Evaluation and Optimization of Trading Strategies. John Wiley & Sons.
Petris, G., and Petrone, S. (2011). State space models in R. Journal of Statistical Software, 41(4), 1–25.
Pfaff, B. (2008). Analysis of Integrated and Cointegrated Time Series with R. Springer.
Pfaff, B., Zivot, E., and Stigler, M. (2022). urca: Unit Root and Cointegration Tests for Time Series Data.
Poon, S.-H., and Granger, C. W. J. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, XLI, 478–539.
Prekopa, A. (1995). Stochastic Programming. Kluwer Academic.
Prigent, J. L. (2007). Portfolio Optimization and Performance Analysis. CRC Press.
Pulley, L. B. (1983). Mean–variance approximations to expected logarithmic utility. Operations Research, 31(4), 685–696.
Qian, E. (2005). Risk parity portfolios: Efficient portfolios through true diversification. PanAgora Asset Management.
Qian, E. (2016). Risk Parity Fundamentals. CRC Press.
Raffinot, T. (2018a). Hierarchical clustering-based asset allocation. The Journal of Portfolio Management, 44(2), 89–99.
Raffinot, T. (2018b). The hierarchical equal risk contribution portfolio. SSRN Electronic Journal.
Razaviyayn, M., Hong, M., and Luo, Z. (2013). A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM Journal on Optimization, 23(2), 1126–1153.
Rockafellar, R. T. (1970). Convex Analysis. Princeton, NJ: Princeton Univ. Press.
Rockafellar, R. T. (1993). Lagrange multipliers and optimality. SIAM Review, 35(2), 183–238.
Rockafellar, R. T., and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21–42.
Rockafellar, R. T., and Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26(7), 1443–1471.
Roncalli, T. (2013a). Introducing expected returns into risk parity portfolios: A new framework for tactical and strategic asset allocation. SSRN Electronic Journal.
Roncalli, T. (2013b). Introduction to Risk Parity and Budgeting. Chapman & Hall/CRC.
Roncalli, T., and Weisang, G. (2016). Risk parity portfolios with risk factors. Quantitative Finance, 16(3), 377–388.
Roy, A. (1952). Safety first and the holding of assets. Econometrica, 20(3), 431–449.
Rubinstein, M. (2002). Markowitz’s “portfolio selection”: A fifty-year retrospective. The Journal of Finance, 57(3), 1041–1045.
Rue, H., and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall/CRC.
Ruiz, E. (1994). Quasi-maximum likelihood estimation of stochastic volatility models. Journal of Econometrics, 63(1), 289–306.
Ruppert, D., and Matteson, S. D. (2015). Statistics and Data Analysis for Financial Engineering: With R Examples. Springer.
Ruszczynski, A. P., and Shapiro, A. (2003). Stochastic Programming. Elsevier.
Santamaria, I., Scharf, L. L., Via, J., Wang, H., and Wang, Y. (2017). Passive detection of correlated subspace signals in two MIMO channels. IEEE Transactions on Signal Processing, 65(20), 5266–5280.
Sardarabadi, A. M., and Veen, A. J. van der. (2018). Complex factor analysis and extensions. IEEE Transactions on Signal Processing, 66(4), 954–967.
Savage, L. J. (1954). The Foundations of Statistics. New York: John Wiley & Sons.
Scaillet, O. (2004). Nonparametric estimation and sensitivity analysis of expected shortfall. Mathematical Finance, 14(1), 115–129.
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G. (2009). The graph neural network model. IEEE Transactions on Neural Networks, 20(1), 61–80.
Schaible, S. (1974). Parameter-free convex equivalent and dual programs of fractional programming problems. Zeitschrift Fur Operations Research, 18(5), 187–196.
Scharf, L. L. (1991). Statistical Signal Processing. Addison-Wesley.
Scherer, B. (2002). Portfolio resampling: Review and critique. Financial Analysts Journal, 58(6), 98–109.
Schmidhuber, J. (2015). Deep learning in neural networks: An overview. Neural Networks, 61, 85–117.
Schmidhuber, J. (2022). Annotated history of modern AI and deep learning. Preprint. Available at arXiv.
Scott, R. C., and Horvath, P. A. (1980). On the direction of preference for moments of higher order than the variance. The Journal of Finance, 35(4), 915–919.
Scozzari, A., Tardella, F., Paterlini, S., and Krink, T. (2013). Exact and heuristic approaches for the index tracking problem with UCITS constraints. Annals of Operations Research, 205(1), 235–250.
Scutari, G., Facchinei, F., Song, P., Palomar, D. P., and Pang, J.-S. (2014). Decomposition by partial linearization: Parallel optimization of multi-agent systems. IEEE Transactions on Signal Processing, 62(3), 641–656.
Scutari, G., and Sun, Y. (2018). Parallel and distributed successive convex approximation methods for big-data optimization. In F. Facchinei and J. S. Pang, editors, Multi-agent optimization, pages 141–308. Springer.
Sezer, O. B., Gudelek, M. U., and Ozbayoglu, A. M. (2020). Financial time series forecasting with deep learning: A systematic literature review: 2005–2019. Applied Soft Computing, 90, 106181.
Shalev-Shwartz, S., and Ben-David, S. (2014). Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press.
Shapcott, J. (1992). Index Tracking: Genetic Algorithms for Investment Portfolio Selection. Report EPCC-SS92-24, Edinburgh Parallel Computing Centre, The University of Edinburgh.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442.
Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119–138.
Sharpe, W. F. (1994). The Sharpe ratio. Journal of Portfolio Management, 21, 49–58.
Shen, W., Wang, B., Pu, J., and Wang, J. (2019). The Kelly growth optimal portfolio with ensemble learning. In Proceedings of the AAAI conference on artificial intelligence,Vol. 33, pages 1134–1141.
Shen, W., and Wang, J. (2017). Portfolio selection via subset resampling. In Proceedings of the AAAI conference on artificial intelligence,Vol. 31, pages 1517–1523.
Shiller, R. J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71(3), 421–436.
Shiller, R. J. (2003). From efficient markets theory to behavioral finance. Journal of Economic Perspectives, 17(1), 83–104.
Shumway, R. H., and Stoffer, D. S. (2017). Time Series Analysis and Its Applications. Springer.
Small, C. G. (1990). A survey of multidimensional medians. International Statistical Review, 58(3), 263–277.
Sohl-Dickstein, J., Weiss, E. A., Maheswaranathan, N., and Ganguli, S. (2015). Deep unsupervised learning using nonequilibrium thermodynamics. In Proceedings of the international conference on machine learning (ICML),Vol. 37, pages 2256–2265.
Song, J., Babu, P., and Palomar, D. P. (2015). Sparse generalized eigenvalue problem via smooth optimization. IEEE Transactions on Signal Processing, 63(7), 1627–1642.
Song, Y., and Ermon, S. (2019). Generative modeling by estimating gradients of the data distribution. In Proceedings of the 33rd international conference on neural information processing systems (NeurIPS), pages 11918–11930. Vancouver, Canada.
Spinu, F. (2013). An algorithm for computing risk parity weights. SSRN Electronic Journal.
Srivastava, M. S., and Bilodeau, M. (1989). Stein estimation under elliptical distributions. Journal of Multivariate Analysis, 28(2), 247–259.
Stancu-Minasian, I. M. (1997). Fractional Programming: Theory, Methods and Applications. Dordrecht: Kluwer Academic Publishers.
Stein, C. (1955). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proceedings of the 3rd berkeley symposium on probability and statistics,Vol. Vol. 1, pages (pp. 197–206).
Sturm, J. F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11(1-4), 625–653.
Sun, S., Wang, R., and An, B. (2023). Reinforcement learning for quantitative trading. ACM Transactions on Intelligent Systems and Technology, 13(3), 1–29.
Sun, Y., Babu, P., and Palomar, D. P. (2014). Regularized Tyler’s scatter estimator: Existence, uniqueness, and algorithms. IEEE Transactions on Signal Processing, 62(19), 5143–5156.
Sun, Y., Babu, P., and Palomar, D. P. (2015). Regularized robust estimation of mean and covariance matrix under heavy-tailed distributions. IEEE Transactions on Signal Processing, 63(12), 3096–3109.
Sun, Y., Babu, P., and Palomar, D. P. (2017). Majorization–minimization algorithms in signal processing, communications, and machine learning. IEEE Transactions on Signal Processing, 65(3), 794–816.
Takahashi, S., Chen, Y., and Tanaka-Ishii, K. (2019). Modelling financial time-series with generative adversarial networks. Physica A: Statistical Mechanics and Its Applications, 527, 1–12.
Tasche, D. (2008). Capital allocation to business units and sub-portfolios: The Euler principle. Preprint. Available at arXiv.
Taylor, S. J. (1982). Financial returns modelled by the product of two stochastic processes: A study of daily sugar prices, 1691–79. In O. D. Anderson, editor, Time series analysis: Theory and practice 1, pages 203–226. North-Holland.
Taylor, S. J. (1994). Modeling stochastic volatility: A review and comparative study. Mathematical Finance, 4(2), 183–204.
Thorp, E. O. (1962). Beat the Dealer: A Winning Strategy for the Game of Twenty-One. New York: Blaisdell Publishing.
Thorp, E. O. (1971). Portfolio choice and the Kelly criterion. Business and Economics Statistics Section, Proceedings of the American Statistical Association, 215–224.
Thorp, E. O. (1997). The Kelly criterion in Blackjack, sports betting, and the stock market. In Proceedings of the 10th international conference on gambling and risk taking. Montreal.
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 58(1), 267–288.
Tibshirani, R., Walther, G., and Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 63(2), 411–423.
Triantafyllopoulos, K., and Montana, G. (2011). Dynamic modeling of mean-reverting spreads for statistical arbitrage. Computational Management Science, 8(1–2), 23–49.
Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons.
Tsay, R. S. (2013). Multivariate Time Series Analysis: With R and Financial Applications. John Wiley & Sons.
Tusell, F. (2011). Kalman filtering in R. Journal of Statistical Software, 39(2), 1–27.
Tütüncü, R. H., and Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1), 157–187.
Tütüncü, R. H., Toh, K. C., and Todd, M. J. (2003). Solving semidefinite-quadratic-linear programs using SDPT3. Mathematical Programming. Series B, 95, 189–217.
Tyler, D. E. (1987). A distribution-free \(M\)-estimator of multivariate scatter. The Annals of Statistics, 15(1), 234–251.
Tyler, D. E., and Yi, M. (2020). Lassoing eigenvalues. Biometrika, 107(2), 397–414.
Uysal, A. S., Li, X., and Mulvey, J. M. (2024). End-to-end risk budgeting portfolio optimization with neural networks. Annals of Operations Research, 339(1–2), 397–426.
Vandenberghe, L., and Boyd, S. (1996). Semidefinite programming. SIAM Review, 38(1), 49–95.
Vapnik, V. (1999). The Nature of Statistical Learning Theory. Springer.
Varadhan, R., and Roland, C. (2008). Simple and globally convergent methods for accelerating the convergence of any EM algorithm. Scandinavian Journal of Statistics, 35(2), 335–353.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., … Polosukhin, I. (2017). Attention is all you need. In Proceedings of the 31st international conference on neural information processing systems (NeurIPS), pages 6000–6010.
Vidyamurthy, G. (2004). Pairs Trading: Quantitative Methods and Analysis. John Wiley & Sons.
Vinod, H. D. (2006). Maximum entropy ensembles for time series inference in economics. Journal of Asian Economics, 17, 955–978.
von Neumann, J. (1937). Über ein ökonomisches Gleichgewichtssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. Ergebnisse Eines Mathematischen Kolloquiums, 8, 73–83.
Wan, X., Wang, W., Liu, J., and Tong, T. (2014). Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range. BMC Medical Research Methodology, 14(135), 1–13.
Wang, Q. J. (1996). Direct sample estimators of L moments. Water Resources Research, 32(12), 3617–3619.
Wang, X., Zhou, R., Ying, J., and Palomar, D. P. (2023). Efficient and scalable parametric high-order portfolios design via the skew-\(t\) distribution. IEEE Transactions on Signal Processing, 71, 3726–3740.
Ward, J. H. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236–244.
White, H. (2000). A reality check for data snooping. Econometrica, 68(5), 1097–1126.
Wiesel, A. (2012a). Geodesic convexity and covariance estimation. IEEE Transactions on Signal Processing, 60(12), 6182–6189.
Wiesel, A. (2012b). Unified framework to regularized covariance estimation in scaled Gaussian models. IEEE Transactions on Signal Processing, 60(1), 29–38.
Wiesel, A., and Zhang, T. (2014). Structured robust covariance estimation. Foundations and Trends in Signal Processing, Now Publishers, 8(3), 127–216.
Wuertz, D., Chalabi, Y., Setz, T., Maechler, M., Boudt, C., Chausse, P., … Boshnakov, G. N. (2022). fGarch: Rmetrics – Autoregressive Conditional Heteroskedastic Modelling.
Wuertz, D., Setz, T., Chalabi, Y., Chen, W., and Theussl, S. (2023). fPortfolio: Rmetrics – Portfolio Selection and Optimization.
Xiu, S., and Palomar, D. P. (2023). Intraday volatility–volume joint modeling and forecasting: A state-space approach. In Proceedings of the european signal processing conference (EUSIPCO). Helsinki, Finland.
Xiu, S., Wang, X., and Palomar, D. P. (2023). A fast successive QP algorithm for general mean–variance portfolio optimization. IEEE Transactions on Signal Processing, 71, 2713–2727.
Xu, F., Lu, Z., and Xu, Z. (2016). An efficient optimization approach for a cardinality-constrained index tracking problem. Optimization Methods and Software, 31(2), 258–271.
Xu, F., Ma, J., and Lu, H. (2022). Group sparse enhanced indexation model with adaptive beta value. Quantitative Finance, 22(10), 1905–1926.
Yager, R. R. (1996). Constrained OWA aggregation. Fuzzy Sets and Systems, 81(1), 89–101.
Ye, Y. (1997). Interior Point Algorithms: Theory and Analysis. New York: Wiley & Sons.
Ying, J., Cardoso, J. V. M., and Palomar, D. P. (2020). Nonconvex sparse graph learning under Laplacian constrained graphical model. In Proceedings of the 34th international conference on neural information processing systems (NeurIPS), pages 7101–7113. Virtual.
Ylvisaker, N. D. (1965). The expected number of zeros of a stationary Gaussian process. The Annals of Mathematical Statistics, 36(3), 1043–1046.
Yoon, J., Jarrett, D., and Schaar, M. van der. (2019). Time-series generative adversarial networks. In Proceedings of the 33rd international conference on neural information processing systems (NeurIPS), pages 5508–5518. Vancouver, Canada.
Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), 673–683.
Young, W. E., and Trent, R. H. (1969). Geometric mean approximations of individual security and portfolio performance. Journal of Financial and Quantitative Analysis, 4(2), 179–199.
Zakamouline, V., and Koekebakker, S. (2009). Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance. Journal of Banking and Finance, 33(7), 1242–1254.
Zakamulin, V. (2018). Revisiting the profitability of market timing with moving averages. International Review of Finance, 18(2), 317–327.
Zhang, C., Zhang, Z., Cucuringu, M., and Zohren, S. (2021). A universal end-to-end approach to portfolio optimization via deep learning. Preprint. Available at arXiv.
Zhang, M., Rubio, F., and Palomar, D. P. (2013). Improved calibration of high-dimensional precision matrices. IEEE Transactions on Signal Processing, 61(6), 1509–1519.
Zhang, M., Rubio, F., Palomar, D. P., and Mestre, X. (2013). Finite-sample linear filter optimization in wireless communications and financial systems. IEEE Transactions on Signal Processing, 61(20), 5014–5025.
Zhang, Z., Zohren, S., and Roberts, S. (2020a). Deep learning for portfolio optimization. The Journal of Financial Data Science, 2(4), 8–20.
Zhang, Z., Zohren, S., and Roberts, S. (2020b). Deep reinforcement learning for trading. The Journal of Financial Data Science, 4(1), 1–16.
Zhao, L., Wang, Y., Kumar, S., and Palomar, D. P. (2019). Optimization algorithms for graph Laplacian estimation via ADMM and MM. IEEE Transactions on Signal Processing, 67(16), 4231–4244.
Zhao, Z., and Palomar, D. P. (2018). Mean-reverting portfolio with budget constraint. IEEE Transactions on Signal Processing, 66(9), 2342–2357.
Zhao, Z., Zhou, R., and Palomar, D. P. (2019). Optimal mean-reverting portfolio with leverage constraint for statistical arbitrage in finance. IEEE Transactions on Signal Processing, 67(7), 1681–1695.
Zhou, R., Liu, J., Kumar, S., and Palomar, D. P. (2020). Robust factor analysis parameter estimation. In R. Moreno-Díaz, F. Pichler, and A. Quesada-Arencibia, editors, Computer aided systems theory – EUROCAST 2019, pages 3–11. Springer.
Zhou, R., and Palomar, D. P. (2020). Understanding the quintile portfolio. IEEE Transactions on Signal Processing, 68, 4030–4040.
Zhou, R., and Palomar, D. P. (2021). Solving high-order portfolios via successive convex approximation algorithms. IEEE Transactions on Signal Processing, 69, 892–904.
Zhou, R., Wang, X., and Palomar, D. P. (2022). highOrderPortfolios: Design of High-Order Portfolios via Mean, Variance, Skewness, and Kurtosis.
Zhou, R., Ying, J., and Palomar, D. P. (2022). Covariance matrix estimation under low-rank factor model with nonnegative correlations. IEEE Transactions on Signal Processing, 70, 4020–4030.
Zhu, S., and Fukushima, M. (2009). Worst-case conditional value-at-risk with application to robust portfolio management. Operations Research, 57(5), 1155–1168.
Zibulevsky, M., and Elad, M. (2010). L1–L2 optimization in signal and image processing. IEEE Signal Processing Magazine, 27(3), 76–88.
Zivot, E., Wang, J., and Koopman, S. J. (2004). State space modeling in macroeconomics and finance using SsfPack for S+FinMetrics. In A. Harvey, S. J. Koopman, and N. Shephard, editors, State space and unobserved component models: Theory and applications, pages 284–335. Cambridge University Press.
Zou, H., and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 67(2), 301–320.
Zoubir, A. M., Koivunen, V., Ollila, E., and Muma, M. (2018). Robust Statistics for Signal Processing. Cambridge University Press.