A Stackelberg Game of Backward Stochastic Differential Equations with Applications

Yueyang Zheng () and Jingtao Shi ()
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Yueyang Zheng: Shandong University
Jingtao Shi: Shandong University

Dynamic Games and Applications, 2020, vol. 10, issue 4, No 9, 968-992

Abstract: Abstract This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the stochastic maximum principles of BSDEs and forward–backward stochastic differential equations (FBSDEs), respectively. Then, a linear quadratic (LQ) Stackelberg game of BSDEs is investigated under standard assumptions. The state 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 with the control-independent diffusion term. Two high-dimensional Riccati equations are introduced to represent the state feedback for the optimal control of the leader. The solvability of the four Riccati equations are discussed. Theoretical results are applied to a pension fund problem of two players in the financial market.

Keywords: Stackelberg differential game; Backward stochastic differential equation; Maximum principle; Linear quadratic control; Pension fund; 93E20; 49K45; 49N10; 49N70; 60H10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13235-019-00341-z

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