Partial differential equations for finance

This unit introduces parabolic partial differential equations (PDEs) with financial applications. Basic solutions concepts and properties will be covered. Connections between PDE and probabilistic formulations will be established via the Feynman-Kac formula. Option pricing theory will be explored via the Black-Scholes equation. The dynamic programming principle and theory of stochastic control will be briefly introduced. You will learn to derive relevant PDEs for financial problems, study their properties, and solve using numerical methods such as finite difference methods, Monte-Carlo methods, and deep learning.