Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven By L\'{e}vy Processes

TL;DR

This paper studies a two-player zero-sum stochastic differential game with partial information, involving backward stochastic systems driven by Lévy processes, providing conditions for optimal controls and illustrating with a linear quadratic example.

Contribution

It introduces new theoretical conditions for optimal controls in backward stochastic differential games driven by Lévy processes under partial information.

Findings

Established verification and necessary conditions for optimal controls.

Analyzed a linear quadratic stochastic differential game example.

Extended stochastic game theory to systems driven by Lévy processes.

Abstract

In this paper, we consider a partial information two-person zero-sum stochastic differential game problem where the system is governed by a backward stochastic differential equation driven by Teugels martingales associated with a L\'{e}vy process and an independent Brownian motion. One sufficient (a verification theorem) and one necessary conditions for the existence of optimal controls are proved. To illustrate the general results, a linear quadratic stochastic differential game problem is discussed.