STOCHASTIC REPRESENTATIONS FOR SOLUTIONS TO PARABOLIC DIRICHLET PROBLEMS FOR NONLOCAL BELLMAN EQUATIONS

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)3271-3310
Journal / PublicationAnnals of Applied Probability
Volume29
Issue number6
Publication statusPublished - Dec 2019
Externally publishedYes

Abstract

We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.

Research Area(s)

  • Dynamic programming principle, Hamilton-Jacobi-Bellman equation, Integro-PDE, Lévy process, Stochastic representation formula, Value function, Viscosity solution