Zero-Sum Stochastic Differential Games with Risk-Sensitive Cost

Article

Abstract

Zero-sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics, we completely characterize all possible saddle point strategies in the class of stationary Markov controls. In addition, we also establish existence-uniqueness result for the value function of the Hamilton–Jacobi–Isaacs equation.

Keywords

Stochastic differential games Risk-sensitive payoff Hamilton–Jacobi–Isaacs equations Saddle point strategy Verification result 

Mathematics Subject Classification

Primary: 91A15 Secondary: 91A23 49N70 

Notes

Acknowledgements

We thank the anonymous referees for their careful reading and valuable comments. This research of Anup Biswas was partly supported by an INSPIRE faculty fellowship and a DST-SERB grant EMR/2016/004810. Subhamay Saha acknowledges the hospitality of the Department of Mathematics in IISER-Pune while he was visiting at the early stages of this work.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Science Education and ResearchPuneIndia
  2. 2.Department of MathematicsIndian Institute of TechnologyGuwahatiIndia

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