Cambridge Mathematical Tripos Supervisions

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.