Everything Financial Engineering

Table of Contents

• Finance and Economics
• Statistics and Econometrics
• Pricing
• Trading
• Monte Carlo simulation
• Optimization
• Game Theory
• Machine Learning
• Miscellaneous

Finance and Economics

Investor

• St. Petersburg Paradox
• Utility Functions
• Indifference Curve
• Behavioral Economics

Investment

• Rate of Return
• Volatility
• Value at Risk
• Expected Shortfall

Market

• Efficient Market Hypothesis
• Bond Market
• Yield Curve
• Libor Rate

Returns models

• Modern Portfolio Theory
• CAPM
• Arbitrage Pricing Theory
• Fama French Model

Statistics and Econometrics

Estimators

• Consistent Estimator
• Biasedness

Regression

• Ordinary Least Squares
• Gauss Markov
• Simple and Multiple Regression
• Multivariate Linear Regression
• Transform both sides
• Box Cox Transformation
• Robust Regression
• Least Trimmed Squares
• Local Regression (LOESS)
• Non Parametric Regression

Regression Diagnostics

• Leverage
• Influential Observations
• Errors and Residuals

Statistical Tests

• Null Hypothesis
• t-test
• F-test
• ANOVA

Model Selection

• Maximum Likelihood Estimator
• AIC
• BIC

Time Series Analysis

• ARIMA models
• GARCH models

Misc

• Bayesian Statistics
• Principal Component Analysis

Pricing

Portfolios

• Self-financing Portfolios
• Replicating Portfolios
• Complete Markets

Securities

• Put call Parity
• Options
• Exotic Options
• Futures Contract
• Forward Contract

Stochastic Calculus

• Brownian Motion / Wiener Process
• Ito's Lemma
• Feynman Kac
• Fokker Planck

Models

• Lattice Model
• Binomial Option Pricing Model
• Black Scholes
• Greeks
• Arbitrage

Trading

Market

• Bid Ask Spread
• Slippage

Stochastic Optimal Control

• Stochastic Optimal Control
• HJB equation
• Bellman Equation

Strategies

• Constant Mix
• Buy and Hold
• Merton's portfolio problem
• Black Litterman
• Return Based Style Analysis
• Risk Parity
• Momentum Investing
• Mean Reversion
• Sell in May
• Pairs Trading

Testing Strategies

• Back Testing

Execution

• Optimal Execution by Almgren-Chriss

Monte Carlo simulation

• Law of Large Numbers
• Inverse Transform Sampling
• Rejection Sampling
• Importance Sampling
• Markov Chain Monte Carlo
• Option Pricing using Monte Carlo
• Rao-Blackwell

Optimization

• Convex Optimization
• Duality
• NP Completeness

Programming

• Linear Programming
• Simplex Method
• Nonlinear Programming
• Integer Programming
• Stochastic Programming

Heuristic Based

• Genetic Algorithms
• Simulated Annealing
• Ant Colony

Game Theory

• Simultaneous Games
• Sequential Games
• Strategies
• Nash Equilibria
• Complete Information
• Perfect Information
• Lemke Howson Algorithm
• Minimax Algorithm
• Evolutionary Game Theory
• Replicator Equation

Games

• Zero Sum Games
• Repeated Games
• Prisoner's Dilemma
• Battle of Sexes

Machine Learning

Supervised Learning

• K-Nearest Neighbors
• Naive Bayes
• Random Forest
• Support Vector Machine
• Logistic Regression
• Artificial Neural Network
• Deep Learning

Unsupervised Learning

• K-Means
• K-Medoids

Regression

Reinforcement Learning

• Markov Decision Process
• Apprenticeship Learning

Miscellaneous

• Expectation Maximization
• Optimal Stopping
• Secretary Problem
• Markov Chains and Stationary Distributions
• Hidden Markov Models