隨機Filtering理論及其在財務數學上的應用

Abstract

In this project we aim to study the stochastic ¯ltering theory and its applications. Stochas- tic ¯ltering theory is widely applied in several ¯elds, for example, the ¯nancial mathematics, physics, aerospace engineering, and military. We focus on investigating its applications to ¯nancial mathematics, in particular, in the robust utility optimization problem in partial in- formation model. In the ¯rst year we discuss a partial information model in the context of ¯nite-state Markov chain and construct an example with explicit solution. In the second year we will study general models.