An Analytic Approach to Purely Nonlocal Bellman Equations Arising in Models of Stochastic Control

Helmut Abels, and Moritz Kassmann
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Submission date: 10. Feb. 2006
Pages: 34
published in: Journal of differential equations, 236 (2007) 1, p. 29-56 
DOI number (of the published article): 10.1016/j.jde.2006.12.013
MSC-Numbers: 35J60, 47G20, 60J75, 93E20
Keywords and phrases: Bellman equation, fully nonlinear equation, ntegro-differential operator, Markov jump process, stochastic control
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Abstract:
Given a bounded domain and two integro-differential operators of the form we study the fully nonlinear Bellman equation

with Dirichlet boundary conditions. Here, are nonnegative functions. We prove the existence of a nonnegative function which satisfies (0.1) almost everywhere. The main difficulty arises through the nonlocality of and the absence of regularity near the boundary.