FM 5031/2 - Financial Mathematics Practioner Sequence

Module - Risk & Asset Allocation

Instructor - John Dodson

Fall 1 - Introduction & Random Variables

• Introduction
• Meucci's Program
• Random Variables
• Characterizations
• Transformations
• Expectation
• Law of Large Numbers
• Monte Carlo
• Summary Statistics
• Central Moments
• Normal Distribution
• Central Limit Theorem
• Change of Measure
• Mixtures

Fall 2 - Common Random Variables

• Taxonomy by Support
• Finite
• Countable
• Interval
• Half-line
• Unbounded
• Common Transforms
• Common Mixtures
• Non-Parametric Descriptions

Fall 3 - Dependence

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

Fall 4 - Market Models

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

Fall 5 - Estimators

• Motivation
• Sample
• Sufficient Statistic
• Estimator
• Loss
• Maximum Likelihood Estimator
• Standard Error
• Admissibility

Fall 6 - Conditional Heteroskedasticity

Fall 7 - Real-World Data

• Robustness
• M-Estimators
• Missing Data
• Overlapping Data
• Other Techniques
• Implied Characterization

Spr 1 - Investor Objective & Satisfaction

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

Spr 2 - Mean-Variance Optimization

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

Spr 3 - Bayesian Estimation

• Bayesian Estimation
• Prior
• Pseudo-data
• Bayesian Estimator
• Determining the Prior

Spr 4 - Allocations as Decisions

• Estimation Risk
• Bias & Efficiency in Allocation Decision Strategies
• Prior Strategy
• Sample-based Strategy

Spr 5 - Robust Bayesian Allocation

• Von Neumann-Morenstern Utility
• Minimax Regret
• Michaud Re-sampling
• Black-Litterman Conditioning

Spr 6 - Meucci's Robust Bayesian Allocation