This course aims to introduce important ideas in theory of probability and differential equations, and their applications to mathematical finance. Topics include: Finite Probability Spaces, Continuous probability theory, the Laplace transform, the Fourier transform, the diffusion equation, measure and integration, Brownian motion, Ito’s Lemma, derivation of the Black-Scholes equation.

CILO-1: Familiar with the mathematical foundations supporting various models in modern finance theories, such as stochastic models for asset prices and no‐arbitrage‐based pricing models for derivative securities. CILO-2: Familiar with the Merton model yielding optional portfolios and consumption plans. CILO-3: Develop skills to interpret and apply interest rate models, e.g., Vasicek models. CILO-4: Develop skills to apply Black-Scholes model to design hedging strategies and identify the impact of transaction costs on the hedging process.