Cambridge Mathematical Tripos Supervisions
Undergraduate course, CMS, University of Cambridge, 2024
I supervised five third year undergraduates in the Part II course ‘Stochastic Financial Models’. I had the responsibility of discussing students’ submissions to problem sets (can be found here) and more general questions regarding the material.
Indicative syllabus
- Standing Assumptions and Notation: Assumptions about financial markets and asset prices; definitions of market setup.
- One-Period Model: Investor wealth and random asset prices; mean-variance analysis and portfolio optimization.
- Market Portfolio and Mutual Fund Theorem: Market portfolio definition; efficient frontier formulation.
- Capital Asset Pricing Model (CAPM): Assumptions and derivation; risk-return relationship.
- Expected Utility Hypothesis: Utility functions, preferences, and risk aversion measures.
- State Price Densities: Definition, derivation, and relationship to utility maximization.
- Risk Neutral Measures: Concept, applications in pricing, and equivalent measures.
- Arbitrage and Fundamental Theorem of Asset Pricing: Arbitrage definition and implications; fundamental theorem proof.
- Utility Maximization in Binomial Models: Optimal portfolios and contingent claim pricing.
- Multi-Period Models: Filtrations, adapted processes, and conditional expectations.
- Stopping Times and Optional Stopping Theorem: Definitions, applications, and proofs.
- Martingale Theory: Martingale transforms, examples, and properties.
- Pricing and Hedging of Derivatives: Attainable claims, no-arbitrage prices, and examples.
- Advanced Topics: Filtrations, sigma-algebras, and conditional probability.