On Zero-Sum Stochastic Differential Games

Details On Zero-Sum Stochastic Differential Games On Zero-Sum Stochastic Differential Games

2011-12-24

arxiv.org/abs/1112.5744v3

Mathematics

Optimization and Control

Key Words: Zero-sum stochastic differential games, Elliott-Kalton strategies, dynamic programming principle, stability under p

Scientific paper

We generalize the results of Fleming and Souganidis (1989) on zero sum stochastic differential games to the case when the controls are unbounded. We do this by proving a dynamic programming principle using a covering argument instead of relying on a discrete approximation (which is used along with a comparison principle by Fleming and Souganidis). Also, in contrast with Fleming and Souganidis, we define our pay-off through a doubly reflected backward stochastic differential equation. The value function (in the degenerate case of a single controller) is closely related to the second order doubly reflected BSDEs.

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