A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance

TL;DR

This paper studies a complex stochastic differential game with partial observations, deriving conditions for Nash equilibrium and applying the results to a financial investment problem using filtering theory.

Contribution

It introduces a new framework for partially observed non-zero sum stochastic differential games involving forward-backward SDEs and provides explicit investment strategies.

Findings

Derived maximum principle as necessary condition for Nash equilibrium

Provided verification theorem as sufficient condition

Applied results to explicit financial investment strategies

Abstract

In this article, we concern a kind of partially observed non-zero sum stochastic differential game based on forward and backward stochastic differential equations (FBSDEs). It is required that each player has his own observation equation, and the corresponding open-loop Nash equilibrium control is required to adapted to the filtration that the observation process generated. To find this open-loop Nash equilibrium point, we prove the maximum principle as a necessary condition of the existence of this point, and give a verification theorem as a sufficient condition to verify it is the real open-loop Nash equilibrium point. Combined this with reality, a financial investment problem is raised. We can obtain the explicit observable investment strategy by using stochastic filtering theory and the results above.