Abstract:  This paper deals with the problem of exponential utility maximization in a model where the risky asset price S is a geometric marked point process whose dynamics depend on another process X, referred to as the stochastic factor. The process X is modeled as a jump diffusion process which may have common jump times with S. The classical dynamic programming approach leads to characterize the value function as a solution of the HamiltonJacobiBellman equation. The solution together with the optimal strategy can be computed under suitable assumptions. Moreover, an explicit representation of the density of the minimal entropy measure (MEMM) and a duality result which gives a relationship between the utility maximization problem and the MEMM are given. This duality result is obtained for a class of strategies greater than those usually considered in literature. A discussion on the pricing of a European claim by the utility indifference approach and its asymptotic variant is performed.
