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In this study, we consider the exponential utility maximization problem inthe context of a jump-diffusion model. To solve the problem, we rely on thedynamic programming principle and we derive from it a quadratic BSDE withjumps. Since this quadratic BSDE is driven both by a Wiener process and by aPoisson random measure having a Levy measure with infinite mass, our main taskconsists in establishing a new existence result for the specific BSDEintroduced.

An extended existence result for quadratic BSDEs with jumps with application to the utility maximization problem