Stochastic Optimal Control and BSDEs with Logarithmic Growth

TL;DR

This paper investigates the existence of optimal controls and saddle-points in stochastic differential games using backward stochastic differential equations with logarithmic growth, establishing existence and uniqueness results.

Contribution

It introduces a novel analysis of BSDEs with logarithmic growth in the context of stochastic control and differential games, proving existence and uniqueness of solutions.

Findings

Existence of optimal strategies for stochastic control problems.

Existence and uniqueness of solutions to BSDEs with logarithmic growth.

Application to zero-sum stochastic differential games.

Abstract

In this paper, we study the existence of an optimal strategy for the stochastic control of diffusion in general case and a saddle-point for zero-sum stochastic differential games. The problem is formulated as an extended BSDE with logarithmic growth in the $z$-variable and terminal value in some $L^p$ space. We also show the existence and uniqueness of solution of this BSDE.