61 research outputs found
The obstacle problem for semilinear parabolic partial integro-differential equations
This paper presents a probabilistic interpretation for the weak Sobolev
solution of the obstacle problem for semilinear parabolic partial
integro-differential equations (PIDEs).
The results of Leandre (1985) concerning the homeomorphic property for the
solution of SDEs with jumps are used to construct random test functions for the
variational equation for such PIDEs. This results in the natural connection
with the associated Reflected Backward Stochastic Differential Equations with
jumps (RBSDEs), namely Feynman Kac's formula for the solution of the PIDEs.
Moreover it gives an application to the pricing and hedging of contingent
claims with constraints in the wealth or portfolio processes in financial
markets including jumps.Comment: 31 page
Approximate solutions for a class of doubly perturbed stochastic differential equations
In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carathéodory approximate solution converges to the solution of DPSDEs under the global Lipschitz condition. Moreover, we extend the above results to the case of DPSDEs with non-Lipschitz coefficients
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