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. Deriva

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