Mathematical Finance

9.

Portfolio Theory and Optimization

9.1.

Mean-Variance Optimization

9.1.1.

Markowitz Framework

9.1.1.1.

Expected Return Vector

9.1.1.2.

Covariance Matrix

9.1.1.3.

Optimization Problem

9.1.2.

Efficient Frontier

9.1.2.1.

9.1.2.2.

Two-Fund Theorem

9.1.3.

Capital Asset Pricing Model

9.1.3.1.

Market Portfolio

9.1.3.2.

Security Market Line

9.1.3.3.

Beta Coefficient

9.1.3.4.

CAPM Applications

9.1.4.

Extensions and Criticisms

9.1.4.1.

Multi-Factor Models

9.1.4.2.

Arbitrage Pricing Theory

9.1.4.3.

Behavioral Critiques

9.2.

Dynamic Portfolio Optimization

9.2.1.

Merton's Portfolio Problem

9.2.1.1.

Continuous-Time Framework

9.2.1.2.

Hamilton-Jacobi-Bellman Equation

9.2.1.3.

Optimal Portfolio Weights

9.2.1.4.

Consumption-Investment Problem

9.2.2.

Stochastic Control Methods

9.2.2.1.

Dynamic Programming

9.2.2.2.

Martingale Methods

9.2.2.3.

Duality Approach

9.2.3.

9.2.3.1.

Transaction Costs

9.2.3.2.

Portfolio Constraints

9.2.3.3.

Incomplete Markets

9.3.

Risk Budgeting and Allocation

9.3.1.

9.3.2.

Risk Budgeting Techniques

9.3.3.

Factor-Based Allocation

9.3.4.

Alternative Risk Measures

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