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arXiv · 1607.00638

Time-Inconsistent Stochastic Linear-quadratic Differential Game

Qinglong Zhou·Gaofeng Zong
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Abstract

We consider a general time-inconsistent stochastic linear-quadratic differential game. 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 derived a sufficient conditions for equilibrium strategies via a system of forward-backward stochastic differential equations. 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.

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Qinglong Zhou, Gaofeng Zong. 2016-07-03. Time-Inconsistent Stochastic Linear-quadratic Differential Game. https://doi.org/10.3934/era.2022131

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