Empirical Finance

Syllabus

• General optimal stopping problems and their applications in financial modelling.
• Finite-difference methods for option pricing: explicit schemes, convergence and numerical stability.
• The Crank-Nicolson method and implicit-explicit approaches to solving pricing equations.
• Perpetual American options: free-boundary problems and optimal exercise rules.
• Perpetual Russian options and advanced examples of optimal stopping in finance.
• The Merton stochastic control problem: optimal portfolio choice and consumption under uncertainty.
• Variance reduction techniques in Monte Carlo simulation.
• Delta-gamma approximation methods for risk measurement and derivative pricing.
• The Gaver-Stehfest algorithm and numerical inversion techniques in financial applications.