The course consists of two parts.

Part 1: Mathematical Finance in Discrete Time: The model, selffinancing strategies and arbitrage, martingales, fundamental theorem of asset prices, binomial model and convergence to Black Scholes, American optionsand optimal stopping,. This part will also contain a revision of the necessary tools from probability theory such as
conditional expectations.

Part 2: Basics of Continuous-Time Finance: Stochastic processes and stopping times, Brownian motion, quadratic variation, pathwise Ito calculus, Black Scholes model, PDE approach to derivative pricing, HJB equation and stochastic control.