Asset allocation and optimal selling rule with regime switching and partial observation

Regime Switching model was receiving increasing attention as researchers searching good models to capture prices of financial assets. Using a regime switching model we study asset allocation problem with one risk free asset and one risky asset. We characterize the value function in terms of solutions of a partial differential equation. We use Viscosity solution and Markov chain approximation for its numerical solution. The second part is concernedwith stock selling rule. We use our regime switching model to find the optimal timing to sell under a logarithmic utility function.A key component in this thesis is that we consider the models with partial information. We resort to Wonham filter to recover necessary information required for optimal control of the problems under consideration.