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Zero-sum stochastic differential games and backward equations. (English) Zbl 0877.93125

Summary: We are concerned with the applications to stochastic zero-sum differential games of the results on backward stochastic differential equations. Using these techniques the existence of a saddle point in the bounded case is obtained if the Isaacs’ condition holds. Furthermore, this technique is also a very simple approach for the existence of an optimal strategy in the case of controlled diffusions.

MSC:

91A60 Probabilistic games; gambling
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