Stochastic target games with controlled loss. (English) Zbl 1290.49075
Summary: We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian uncertainty.
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 |
| 91A15 | Stochastic games, stochastic differential games |
| 91A23 | Differential games (aspects of game theory) |
| 93E20 | Optimal stochastic control |
Keywords:
stochastic target; stochastic game; geometric dynamic programming principle; viscosity solutionReferences:
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