\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

Chapter 5 Financial Data: Graphs

“Mankind invented a system to cope with the fact that we are so intrinsically lousy at manipulating numbers. It’s called the graph.”

— Charlie Munger

Graphs provide a convenient and compact way to represent data while highlighting the relationships between entities of a network. They constitute a powerful mathematical tool with broad applicability in numerous fields, such as biology, brain modeling, finance, statistical physics, management, behavioral modeling, machine learning, social networks, and data science in general. Given the recent availability of large amounts of data collected in a variety of application domains, graph-based analysis plays a fundamental role in understanding and analyzing the structure of large networks that generate data. In practical scenarios, the underlying graph structure that represents the network is often unknown and has to be inferred from the data. Many graph learning algorithms have been proposed during the past two decades, with a recent interest in the past few years. This chapter explores a broad range of graph estimation algorithms, emphasizing recent advances specifically tailored to financial data.

This material will be published by Cambridge University Press as Portfolio Optimization: Theory and Application by Daniel P. Palomar. This pre-publication version is free to view and download for personal use only; not for re-distribution, re-sale, or use in derivative works. © Daniel P. Palomar 2024.