A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem

In this study, we consider the exponential utility maximization problem in the context of a jump–diffusion model. To solve this problem, we rely on the dynamic programming principle to express the value process of this problem in terms of the solution of a quadratic BSDE with jumps. Since the quadratic BSDE11The notation of quadratic BSDE refers to the growth with respect to the variable z of the generator f : ( s , z , u ) → f ( s , z , u ) . study is driven by both a Wiener process and a Poisson random measure having a Lévy measure with infinite mass, our main task is therefore to establish a new existence result for the specific BSDE introduced.