A non-linear PDE for XVA by forward Monte Carlo

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In this article, a solution to a semi-linear PDE is obtained by taking the minimum of solutions to related linear PDEs over an infinite-dimensional space of discount boundaries. By restricting the minimum to a parameterised subset of boundaries, a practical algorithm for numerically solving the semi-linear PDE in a forward Monte Carlo is obtained. We also show how to modify the standard CVA algorithms to account for the risky closeout in the section on comparison to riskless closeout DVA

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