Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
Optimization and Control
2012-04-04 v1 Analysis of PDEs
Probability
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.
Cite
@article{arxiv.1204.0568,
title = {Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation},
author = {Jiongmin Yong},
journal= {arXiv preprint arXiv:1204.0568},
year = {2012}
}
Comments
51 pages