On a Class of Quadratic Growth RBSDE with Jumps and Its Application

Abstract

In this article, we consider a utility maximization problem in a market with jumps and investor trading strategies under constraints. By adopting a dynamic method, we deduce a specific quadratic reflected backward stochastic differential equation (RBSDE) with jumps. We make two contributions: (1) we obtain the existence and uniqueness theorem for the RBSDE; (2) we obtain the price of an American contingent claim in the sense of utility maximization.