Stochastic games with jumps

In the talk we will study zero-sum two-player stochastic differential games with jumps with the help of theory of Backward Stochastic Differential
Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis by considering cost functionals defined
by controlled BSDEs with jumps and by allowing the admissible control processes to depend on events occurring before the beginning of the game (which implies that the cost functionals become random variables), on the other hand the
application of BSDE methods, in particular that of the notion of stochastic ``backward semigroups" introduced by Peng allows to prove a dynamic programming principle for the upper and the lower value functions of the game in a
straight-forward way, without passing by additional approximations. The upper and the lower value functions are proved to be the unique viscosity solutions of the upper and the lower Hamilton-Jacobi-Bellman-Isaacs equations
with differential/difference operator of second order, respectively. For this Peng's BSDE method is translated from the framework of stochastic control theory into that of stochastic differential games with jumps.