A Minimal Book Example
1
Probability Review
1.1
Basic Probability and Counting
1.2
Random Variables
1.3
Moments
1.4
Famous Distributions
1.5
Miscellaneous
1.5.1
Covariance and Correlation
1.5.2
Joint and Conditional Distributions
1.5.3
Adam and Eve
2
R
2.1
Applies
2.2
data.table
2.3
time series
2.4
ggplot
2.5
Optimizers (optim)
2.6
Recursion
2.7
Styling
3
Stochastic Properties
3.1
Stochastic Definitions
3.2
Properties
3.2.1
Stationarity
3.2.2
Martingales
3.2.3
Joint Stochastic Processes
3.2.4
Markov Property
3.2.5
Reflective Property
4
Random Walks
4.1
Gaussian Random Walk
4.1.1
Strong Stationarity
4.1.2
Weak Stationarity
4.1.3
Martingale
4.1.4
Markov
4.2
Simple Random Walk
4.2.1
Properties
4.2.2
Barriers
4.2.3
Behavior
4.3
Gambler’s Ruin
4.3.1
Win Probability
4.3.2
Expected Game Length
5
Branching Processes
5.1
Simple Branching Processes
5.2
Probability Generating Functions
5.3
Extinction Probabilities
5.4
Extinction Conditions
5.5
Long-term Population Metrics
6
Kalman Filters
6.1
Introducing Kalman Filters
6.2
Deriving the Kalman Filter
6.3
Exploring the Kalman Filter
7
Black Scholes
7.1
Black Scholes Model
7.2
Deriving Black Scholes
7.2.1
Log-Normal
7.2.2
Risk-Neutral Paradigm
7.2.3
Symmetric Stock
7.2.4
Stock in Risk Neutral Case
7.3
Exploring Black Scholes
References
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References