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.

Keywords:

• Backward stochastic differential equation (BSDE)
• Poisson random measure
• Reflected BSDE (RBSDE)
• Utility maximization

Mathematics Subject Classification:

• Primary 60J75
• Secondary 60G20

ACKNOWLEDGMENTS

This research was supported in part by the Ministry of Education Humanities Social Science Key Research Institute in University Foundation (07JJD910244), NSFC(10771214). The authors would like to thank the anonymous referees and editors of the journal for their comments and valuable suggestions on the presentation. The authors are grateful to Professor Bingyi Jing, Shaoqiang Tang, and Jing Xu for their helpful discussions.