Abstract
In this paper, a class of stochastic set differential equations (SSDEs) disturbed by a continuous local martingale with the Lipschitzian condition is studied. The solutions of SSDEs are set-valued stochastic processes. First, we give some prior inequalities on set valued integrals. Second, the existence and uniqueness theorem of solutions to SSDEs is proven. Moreover, their continuous dependence on initial conditions and a stability property are investigated. Finally, an illustrating example from the mathematical finance is discussed. The main mathematical tool is Gronwall’s inequality.
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