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Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach

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  • Bingyan Han
  • Chi Seng Pun
  • Hoi Ying Wong

Abstract

This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust mean-variance analysis, namely with state- and control-dependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems.

Suggested Citation

  • Bingyan Han & Chi Seng Pun & Hoi Ying Wong, 2023. "Robust Time-inconsistent Linear-Quadratic Stochastic Controls: A Stochastic Differential Game Approach," Papers 2306.16982, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2306.16982
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    References listed on IDEAS

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