Communications in Information & Systems

Risk sensitive stochastic control and differential games

Wendell H. Fleming

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Abstract

We give a concise introduction to risk sensitive control of Markov diffusion processes and related two-controller, zero-sum differential games. The method of dynamic programming for the risk sensitive control problem leads to a nonlinear partial differential equation of Hamilton-Jacobi-Bellman type. In the totally risk sensitive limit, this becomes the Isaacs equation for the differential game. There is another interpretation of the differential game using the Maslov idempotent probability calculus. We call this a max-plus stochastic control problem. These risk sensitive control/differential game methods are applied to problems of importance sampling for Markov diffusions.

Article information

Source
Commun. Inf. Syst., Volume 6, Number 3 (2006), 161-177.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.cis/1183728983

Mathematical Reviews number (MathSciNet)
MR2347283

Zentralblatt MATH identifier
1132.93049

Citation

Fleming, Wendell H. Risk sensitive stochastic control and differential games. Commun. Inf. Syst. 6 (2006), no. 3, 161--177. https://projecteuclid.org/euclid.cis/1183728983


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