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MCRF

In this paper we
investigate classical solution of a semi-linear system of backward
stochastic integral partial differential equations driven by a
Brownian motion and a Poisson point process. By proving an
Itô-Wentzell formula for jump diffusions as well as an abstract
result of stochastic evolution equations, we obtain the stochastic
integral partial differential equation for the inverse of the
stochastic flow generated by a stochastic differential equation
driven by a Brownian motion and a Poisson point process. By
composing the random field generated by the solution of a backward
stochastic differential equation with the inverse of the stochastic
flow, we construct the classical solution of the system of backward
stochastic integral partial differential equations. As a result, we
establish a stochastic Feynman-Kac
formula.

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