Recent advances in nonlinear filtering with a financial application to derivatives hedging under incomplete information

In this chapter we present some recent results about nonlinear filtering for jump diffusion signal and observation driven by correlated Brownian motions an having common jump times. We provide the Kushner-Stratonovich and the Zakai equation for the normalized and the unnormalized filter respectively. Moreover we give conditions under which pathwise uniqueness for the solutions of both equations holds. Finally we study an application of nonlinear filtering to the financial problem of derivatives hedging in an incomplete market with partial observation. Precisely, we consider the risk minimizing hedging approach. In this framework we compute the optimal hedging strategy for an informed investor and a partially informed one and compare the total expected squared costs of the strategies.