FM 5031 - Financial Mathematics Practioner Sequence

Module - Portfolio Optimization

Instructor - John Dodson

Fall 1 - Introduction & Random Variables

• Introduction
• Course
• Module
• Summary
• Random Variables
• Characterizations
• Transformations
• Expectation
• Law of Large Numbers
• Monte Carlo
• Summary Statistics
• Central Moments
• Normal Distribution
• Central Limit Theorem
• Change of Measure
• Mixtures
• Taxonomy

Fall 2 - Dependence

• Independence
• Conditioning & Margining
• Exercise: Bivariate Normal
• Dependence
• Copulae
• Concordance
• Bayes' Rule
• Covariance
• Cholesky Decomposition
• Spectral Decomposition
• Mahalanobis Distance
• Multivariate Distributions

Fall 3 - Market Models

• Modeling the Market
• Securities Markets
• Market Conventions
• Investment Horizon
• Quest for Invariance
• Identifying Invariants
• Projecting Invariants
• Mapping Invariants
• Sample Problems
• Postscript

Fall 4 - Estimators

• Motivation
• Contest
• Sample
• Sufficient Statistic
• Estimator
• Loss
• Maximum Likelihood Estimator
• Standard Error
• Bayesian Estimation
• Prior
• Pseudo-Data
• Bayesian Estimator

Fall 5 - Evaluating Allocations

• Motivation
• Objectives
• Delta-Gamma
• Satisfaction
• Coherent Properties
• Value-at-Risk
• Expected Shortfall
• Expected Utility

Fall 6 - Mean-Variance Optimization

• Constraints
• Optimization
• Dimension Reduction
• Analytical Solution
• Log-Normal Model
• Time Scaling
• Benchmarks

Fall 7- Bayesian Optimization

• Motivation
• Von Neumann-Morenstern
• Robust Optimization
• Michaud Re-sampling
• Black-Litterman