A stochastic linear-quadratic differential game with time-inconsistency. (English) Zbl 1514.91013
Summary: We consider a general stochastic linear-quadratic differential game with time-inconsistency. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derive a sufficient condition for equilibrium strategies via a system of forward-backward stochastic differential equation. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given.
MSC:
| 91A15 | Stochastic games, stochastic differential games |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 49N10 | Linear-quadratic optimal control problems |
| 93E20 | Optimal stochastic control |
Keywords:
time-inconsistency; stochastic linear-quadratic differential game; equilibrium strategy; BSDE; forward-backward stochastic differential equationReferences:
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