Reflected BSDEs with logarithmic growth and applications in mixed stochastic control problems

Abstract

In this article we study the existence and the uniqueness of a solution for reflected backward stochastic differential equations in the case when the generator is logarithmic growth in the z-variable $(|z|\sqrt{|\ln (|z|)|})$, the terminal value and obstacle are an $L^p$-integrable, for a suitable p>2. To construct the solution we use localization method. We also apply these results to get the existence of an optimal control strategy for the mixed stochastic control problem in finite horizon.

Keywords:

• Reflected backward stochastic differential equations
• stochastic control
• stochastic differential games

AMS 2000 Classifications subjects:

• 60G40
• 93E05
• 93E20
• 60G99

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported in part by the 'Scientific Research Projects of Ibn Zohr University'. K. Oufdil is supported in part by the National Center for Scientific and Technical Research (CNRST), Morocco.