Time-inconsistentoptimal control problems and the equilibrium HJB equation

Jiongmin Yong

doi:10.3934/mcrf.2012.2.271

Article Contents

2012, Volume 2, Issue 3: 271-329. Doi: 10.3934/mcrf.2012.2.271

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Time-inconsistent optimal control problems and the equilibrium HJB equation

Jiongmin Yong^1,

1.
Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received: March 31, 2012

Revised: April 30, 2012

Published: August 2012

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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 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.

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Mathematics Subject Classification: Primary: 93E20, 49L20, 49N10, 49N70; Secondary: 35Q93,91A23, 91A65.

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