| Abstract: |
| We study the continuity problem at the terminal time of the minimal supersolution of backward stochastic differential equation with singular terminal condition. In the continuous case, where the equation is driven by a Brownian motion we give a general criterion on the generator ensuring continuity up to terminal time. We also prove that the solution has a Malliavin derivative, which is the limit of the derivative of the approximating sequence and provide the asymptotic behavior of this derivative close to the terminal time. We apply this result to the regularity of the related partial differential equationby using the associated integro-partial differential equation. Finally, we prove that if there are jumps (i.e. the operator of the PDE is non local), we observe a propagation of the singularity, contrary to the continuous case (local operator). This talk is based on several joint works with D. Cacitti-Holland and A. Popier. |
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