Time-inconsistent optimal control problems and the equilibrium HJB equation
Copyright policy )Time-inconsistent optimal control problems and the equilibrium HJB equation
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.
51 pages
- University of Central Florida United States
equilibrium Hamilton-Jacobi-Bellman equation, 93E20, 49L20, 49N10, 49N70, 35Q93, stochastic differential equation, PREFERENCES, VOLTERRA INTEGRAL-EQUATIONS, GAMES, Mathematics - Analysis of PDEs, FOS: Mathematics, Equilibrium hamilton-jacobi-bellman equation, Time-inconsistent optimal control problem, Mathematics - Optimization and Control, ECONOMIES, Probability (math.PR), forward-backward, Optimization and Control (math.OC), Applied, equilibrium value function, Forward-backward stochastic differential equation, Equilibrium value function, Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)
equilibrium Hamilton-Jacobi-Bellman equation, 93E20, 49L20, 49N10, 49N70, 35Q93, stochastic differential equation, PREFERENCES, VOLTERRA INTEGRAL-EQUATIONS, GAMES, Mathematics - Analysis of PDEs, FOS: Mathematics, Equilibrium hamilton-jacobi-bellman equation, Time-inconsistent optimal control problem, Mathematics - Optimization and Control, ECONOMIES, Probability (math.PR), forward-backward, Optimization and Control (math.OC), Applied, equilibrium value function, Forward-backward stochastic differential equation, Equilibrium value function, Mathematics, Mathematics - Probability, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).121 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 1% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!