In this lecture we will deal with several topics in applied stochastic calculus and applications in finance. The main part of the lecture is devoted to an introduction to stochastic filtering. Generally speaking, stochastic filtering is a method for dealing with stochastic systems that are affected by unobservable factor processes.  In particular, we will  discuss the well-known Kushner-Stratonovich and Zakai equations for nonlinear filtering for the case where the observation is given by a Brownian motion with  drift, where the drift  depends on the unobservable state variable.  Moreover, we will study finite-dimensional approximations for these equations that can be used for the numerical solution of filter problems. The second part of the lecture is devoted to the solution of optimization problems via dynamic programming and the HJB equation. Financial applications will come from the field of portfolio optimization in models with unobservable drift.

via email at

ruediger.frey@wu.ac.at