Utility maximization in a jump market model

Abstract

In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set of all trading strategies is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. To solve the financial problem, we first prove existence and uniqueness results for the introduced BSDE. This allows to give the expression of the value function and characterize optimal strategies for the problem.

Keywords:

• utility maximization
• backward stochastic differential equations (BSDE) with jumps
• stochastic exponential
• BMO martingale

MSC Classification (2000):

• 91B28
• 91B16
• 60H10

Notes

¹ Since the increments of the generator f are computed on the trajectories of predictable processes, (8) is the expression of the process we are interested in, especially in the proof of the uniqueness result.