Reflected BSDEs with Logarithmic Growth and Applications in Mixed Stochastic Control Problems

TL;DR

This paper establishes existence and uniqueness results for reflected backward stochastic differential equations with logarithmic growth generators and applies these findings to determine optimal control strategies in mixed stochastic control problems.

Contribution

It introduces new existence and uniqueness results for reflected BSDEs with logarithmic growth generators and applies them to solve mixed stochastic control problems.

Findings

Proved existence and uniqueness of solutions for reflected BSDEs with logarithmic growth.

Applied the theoretical results to identify optimal control strategies.

Utilized localization method to construct solutions.

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.