AMS 4080

This course explores foundational notions and models in financial mathematics. Topics include attainable payoffs, arbitrage, completeness, the law of one price, first and second Fundamental Theorems of Asset Pricing, introduction to discrete-time stochastic calculus, conditional expectations, risk-neutral martingale measures, dynamic replication in the binomial model for European, American and exotic options, general multi-asset multi-period models.