Title: An HJB approach to exponential utility maximisation for jump processes
Authors: Claudia Ceci
Addresses: Dipartimento di Scienze, Universita di Chieti, Viale Pindaro 87, I-65127-Pescara, Italy
Abstract: This paper deals with the problem of exponential utility maximisation 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 modelled as a jump diffusion process which may have common jump times with S. The classical dynamic programming approach leads us to characterise the value function as a solution of the Hamilton-Jacobi-Bellman equation. The solution, together with the optimal trading 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 maximisation 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.
Keywords: jump diffusions; marked point processes; minimal entropy measure; utility maximisation; risky asset prices; Hamilton-Jacobi-Bellman equation; HJB equation; optimal trading strategy; financial risk.
International Journal of Risk Assessment and Management, 2009 Vol.11 No.1/2, pp.104 - 121
Published online: 22 Dec 2008 *Full-text access for editors Access for subscribers Purchase this article Comment on this article