# Non-zero sum differential games of forward-backward stochastic differential delayed equations under partial information and application

## TL;DR

This paper develops a theoretical framework for non-zero sum differential games involving anticipated forward-backward stochastic delayed equations under partial information, deriving conditions for Nash equilibria and applying them to a pension fund management problem.

## Contribution

It introduces a maximum principle and verification theorem for such complex stochastic differential games, including explicit solutions for linear-quadratic cases and an application to pension fund management.

## Key findings

- Derived explicit Nash equilibrium for linear-quadratic systems
- Proved existence and uniqueness of solutions in particular cases
- Applied the theory to a pension fund management scenario

## Abstract

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient verification theorem of the game system by virtue of the duality and convex variational method. We apply the theoretical results and stochastic filtering theory to study a linear-quadratic game system and derive the explicit form of the Nash equilibrium point and discuss the existence and uniqueness in particular cases. As an application, we consider a time-delayed pension fund manage problem with nonlinear expectation and obtain the Nash equilibrium point.