Credits: 3 (3-0-0)
Description
Mathematical construction of Brownian motion and its essential properties, Derivation of Itô-integrals and Itô calculus, Weak and strong solution concepts of SDEs, existence and uniqueness theorems for SDEs, Basic properties of Itô diffusions e.g., Markov, strong Markov property, The generator of a diffusion processes, Dynkin’s formula; Applications to boundary value problem (Kolmogorov’s Backward equation, Feynman-Kac-formula), Optimal stopping (Optimal stopping problems involving an integral, Connection with variational inequalities), Control theory (Hamilton-Jacobi-Bellman Equation, Stochastic control problem with terminal conditions, Existence of optimal control, Stochastic maximum principle) and Mathematical finance (Option pricing).