According to Pham and Quenez [2001] we solve the optimization problem in an incomplete financial market with stochastic volatility under the realistic case of partial information, where the investor observes the asset price only. We obtain a formula of the expected terminal wealth for general utility functions by using the Martingale Duality Approach. Moreover, we give a proof of the existence of an optimal portfolio process for power utility functions according to Larsen [2009]. Assuming the market price of risk is linear Gaussian we get a formula for the optimal portfolio process for general utility functions by using the Kalman-Bucy filter and Malliavin derivatives. This optimal portfolio is not computable and we therefore establish an approximation of this for power utility functions as a new result. Numerical illustrations by applying the Monte Carlo method with Control Variates complete this thesis.     «

According to Pham and Quenez [2001] we solve the optimization problem in an incomplete financial market with stochastic volatility under the realistic case of partial information, where the investor observes the asset price only. We obtain a formula of the expected terminal wealth for general utility functions by using the Martingale Duality Approach. Moreover, we give a proof of the existence of an optimal portfolio process for power utility functions according to Larsen [2009]. Assuming the ma...     »