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2006 Risk sensitive stochastic control and differential games
Wendell H. Fleming
Commun. Inf. Syst. 6(3): 161-177 (2006).


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.


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Wendell H. Fleming. "Risk sensitive stochastic control and differential games." Commun. Inf. Syst. 6 (3) 161 - 177, 2006.


Published: 2006
First available in Project Euclid: 6 July 2007

zbMATH: 1132.93049
MathSciNet: MR2347283

Rights: Copyright © 2006 International Press of Boston


Vol.6 • No. 3 • 2006
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