Verification by stochastic Perron's method in stochastic exit time control problems

Dmitry B. Rokhlin

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arXiv · 1310.8411

Verification by stochastic Perron's method in stochastic exit time control problems

Dmitry B. Rokhlin

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Abstract

We apply the Stochastic Perron method, created by Bayraktar and Sîrbu, to a stochastic exit time control problem. Our main assumption is the validity of the Strong Comparison Result for the related Hamilton-Jacobi-Bellman (HJB) equation. Without relying on Bellman's optimality principle we prove that inside the domain the value function is continuous and coincides with a viscosity solution of the Dirichlet boundary value problem for the HJB equation.

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Dmitry B. Rokhlin. 2013-10-31. Verification by stochastic Perron's method in stochastic exit time control problems. https://arxiv.org/abs/1310.8411

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