A stochastic maximum principle for backward control systems with random default time

Abstract

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Keywords:

• stochastic maximum principle
• backward control systems
• random default time
• backward stochastic differential equations

Acknowledgement

The authors would like to thank the referees for helpful comments.