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Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach

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  • In this paper, we investigate a class of time-inconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. We study these problems within the game theoretic framework, and look for open-loop Nash equilibrium controls. Under suitable conditions, we derive a verification theorem for equilibrium controls via a flow of forward-backward stochastic partial differential equations. To illustrate our results, we discuss a mean-variance problem with a state-dependent trade-off between the mean and the variance.

    Mathematics Subject Classification: Primary: 91B51, 93E20, 60H30, 93E99, 60H10; Secondary: 93E25.

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