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Ghosh, Mrinal K.; Pradhan, Somnath

Risk-sensitive stochastic differential games with reflecting diffusions. (English) Zbl 1407.91037

Stochastic Anal. Appl. 36, No. 1, 1-27 (2018).
Summary: We study risk-sensitive differential games for controlled reflecting diffusion processes in a bounded domain. We consider both nonzero-sum and zero-sum cases. We treat two cost evaluation criteria; namely, discounted cost and ergodic cost. Under certain assumptions we establish the existence of Nash/saddle-point equilibria for relevant cases.

Cited in 6 Documents

MSC:

91A15 Stochastic games, stochastic differential games
91A23 Differential games (aspects of game theory)
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences

Keywords:

reflected diffusion processes; risk sensitive criteria; stochastic differential games; Hamilton-Jacobi-Isaacs equations; Nash/saddle point equilibria
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References:

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