INFINITE HORIZON REFLECTED BACKWARD STOCHASTIC
DIFFERENTIAL EQUATIONS AND APPLICATIONS IN MIXED CONTROL
AND GAME PROBLEMS
S. Hamadčne
J.-P. Lepeltier
Zhen Wu
Abstract: We prove existence and uniqueness results of the solution for infinite horizon
reflected backward stochastic differential equations with one or two barriers. We also apply
these results to get the existence of optimal control strategy for the mixed control problem
and a saddle-point strategy for the mixed game problem when, in both situations, the horizon
is infinite.
1991 AMS Mathematics Subject Classification: 60H10, 93E05, 93E20.
Key words and phrases: Backward stochastic differential equation, Infinite horizon,
Reflected barriers, Stochastic optimal control, Stochastic differential game.