Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems

TL;DR

This paper studies infinite horizon jump-diffusion forward-backward stochastic differential equations, establishing foundational theorems and applying them to solve linear-quadratic control and game problems with explicit solutions.

Contribution

It provides existence, uniqueness, stability, and comparison theorems for these equations and applies them to derive explicit solutions for control and game problems.

Findings

Established existence and uniqueness of solutions.

Derived stability and comparison results.

Obtained explicit optimal controls and Nash equilibria.

Abstract

In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison theorem for solutions to such kind of equations. Then the theoretical results are applied to study a kind of infinite horizon backward stochastic linear-quadratic optimal control problems, and then differential game problems. The unique optimal controls for the control problems and the unique Nash equilibrium points for the game problems are obtained in closed forms.