Dipartimento di Scienze
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Title:An HJB approach to exponential utility maximization for jump processes
Author(s):Claudia Ceci
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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 Hamilton-Jacobi-Bellman 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.