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Time-Inconsistent Stochastic Linear-quadratic Differential Game

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  • Qinglong Zhou
  • Gaofeng Zong

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. "Time-Inconsistent Stochastic Linear-quadratic Differential Game," Papers 1607.00638, arXiv.org.
    • Handle: RePEc:arx:papers:1607.00638
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    References listed on IDEAS

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    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    2. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
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    9. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2015. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Papers 1504.01152, arXiv.org, revised May 2015.
    10. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2015. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Working Papers hal-01139343, HAL.
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