Forward-backward stochastic differential equations and linear-quadratic generalized Stackelberg games. (English) Zbl 1417.91150
Summary: A multilevel self-similar domination-monotonicity structure is proposed, and a kind of coupled forward-backward stochastic differential equations (FBSDEs) with such structure is proved to be uniquely solvable. Then, this kind of FBSDEs is used to characterize the unique equilibrium of a linear-quadratic generalized Stackelberg game with multilevel hierarchy in a closed form.
MSC:
| 91A65 | Hierarchical games (including Stackelberg games) |
| 93E20 | Optimal stochastic control |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 49N10 | Linear-quadratic optimal control problems |
Keywords:
forward-backward stochastic differential equation; linear-quadratic problem; generalized Stackelberg game; stochastic optimal controlReferences:
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