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Time-inconsistent optimal control problems and the equilibrium HJB equation

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  • A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value function of the problem. Well-posedness such an equation is studied, and time-consistent equilibrium strategies are constructed. As special cases, the linear-quadratic problem and a generalized Merton's portfolio problem are investigated.
    Mathematics Subject Classification: Primary: 93E20, 49L20, 49N10, 49N70; Secondary: 35Q93,91A23, 91A65.

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