ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS, WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS, AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO- DIFFERENTIAL EQUATIO

摘要

The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.