2012/10/11 by Alain Bensoussan, Bensoussan, Alain, Shaokuan Chen +3 · 3 citations
Economics, Econometrics and Finance · #Climate Change Policy and Economics #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1210.3124
openalex publication_date 2012/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper obtains the maximum principle for both stochastic (global)\nopen-loop and stochastic (global) closed-loop Stackelberg differential games.\nFor the closed-loop case, we use the theory of controlled forward-backward\nstochastic differential equations to derive the maximum principle for the\nleader's optimal strategy. In the special case of the open-loop linear\nquadratic Stackelberg game, we consider the follower's Hamiltonian system as\nthe leader's state equation, derive the related stochastic Riccati equation,\nand show the existence and uniqueness of the solution to the Riccati equation\nunder appropriate assumptions. However, for the closed-loop linear quadratic\nStackelberg game, we can write the related Riccati equation consisting of\nforward-backward stochastic differential equations, while leaving the existence\nof its solution as an open problem.\n