Portfolio Optimization under a Partially Observed Jump-diffusion Model

This paper studies the question of maximizing terminal wealth from expected utility in a multidimensional jump-diffusion model. The special feature of our approach is that the investor only observes the vector of stock prices, therefore leading to a partial information framework. Using non-linear filtering and change of measure techniques, we show that the optimization problem can be rewritten such that parameters depend only on the past history of observed prices. Through duality approach, we derive the optimal value function. As examples, special attention is given to three standard utility functions for which we exhibit the optimal value functions. Mathematics Subject Classification: 60G48, 60G35, 90E11. JEL Classification: G11.