期刊
MATHEMATICAL CONTROL AND RELATED FIELDS
卷 2, 期 3, 页码 271-329出版社
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/mcrf.2012.2.271
关键词
Time-inconsistent optimal control problem; equilibrium value function; equilibrium Hamilton-Jacobi-Bellman equation; forward-backward stochastic differential equation
资金
- NSF [DMS-1007514]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007514] Funding Source: National Science Foundation
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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