Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle
Said Hamadène, Universite du Maine
Youssef Ouknine, Universite Cadi Ayyad
Abstract
In this paper we give a solution for the one-dimensional reflected
backward stochastic differential equation when the noise is driven
by a Brownian motion and an independent Poisson point process. We
prove existence and uniqueness of the solution in using
penalization and the Snell envelope theory. However both methods
use a contraction in order to establish the result in the general
case. Finally, we highlight the connection of such reflected BSDEs
with integro-differential mixed stochastic optimal control.
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