Optimal Control of Jump-Markov Processes and Viscosity Solutions

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We investigate the Bellman equation that arises in the optimal control of Markov processes. This is a fully nonlinear integro-differential equation. The notion of viscosity solutions is introduced and then existence and uniqueness results are obtained. Also, the connection between the optimal control problem and the Bellman equation is developed.

This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation and the Office of Naval Research.
This research was completed while the author was visiting the Institute for Mathematics and its Applications.