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Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation (1204.0568v1)

Published 3 Apr 2012 in math.OC, math.AP, and math.PR

Abstract: 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 and some properties of 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.