A Stackelberg Game of Backward Stochastic Differential Equations with Partial Information

TL;DR

This paper studies a Stackelberg game involving backward stochastic differential equations under partial information, providing optimality conditions and explicit solutions for linear-quadratic cases, with applications to pension fund management.

Contribution

It introduces a novel framework for Stackelberg games with partial information in BSDEs and derives explicit Riccati-based solutions for linear-quadratic cases.

Findings

Derived necessary and sufficient optimality conditions for both players.

Provided explicit state feedback control representations via Riccati equations.

Applied the theoretical results to a pension fund management scenario.

Abstract

This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-$\sigma$-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.