Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations

Ruoting Gong; Chenchen Mou; Andrzej Swiech

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arXiv · 1709.00193

Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations

Ruoting Gong·Chenchen Mou·Andrzej Swiech

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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.

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BibTeX RIS

Ruoting Gong, Chenchen Mou, Andrzej Swiech. 2017-09-01. Stochastic Representations for Solutions to Parabolic Dirichlet Problems for Nonlocal Bellman Equations. https://arxiv.org/abs/1709.00193

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