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Nash equilibrium payoffs for stochastic differential games with reflection. (English) Zbl 1283.49043
Summary: In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

MSC:
49N70 Differential games and control
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
91A23 Differential games (aspects of game theory)
91A15 Stochastic games, stochastic differential games
90C39 Dynamic programming
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