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Existence of value in stochastic differential games of mixed type. (English) Zbl 1252.49062

Summary: In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

MSC:

49N70 Differential games and control
60G40 Stopping times; optimal stopping problems; gambling theory
93E20 Optimal stochastic control
49J40 Variational inequalities
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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