What is Feynman-Kac formula?

What is Feynman-Kac formula?

Approach: Link between PDEs and expectations.

Provides representation of solution to certain PDEs as expectation of functional of stochastic process. For ∂u/∂t + μ∂u/∂x + ½σ²∂²u/∂x² - ru = 0 with terminal condition u(T,x)=ψ(x), solution u(t,x)=E[e^{-r(T-t)}ψ(X_T)|X_t=x] where dX=μ dt+σ dW.

Follow-up: Apply to Black-Scholes PDE.

Key concepts: pde, stochastic process, expectation representation.