Motivated by the equations of cross valuation adjustments (XVAs) in the realistic case where capital is deemed fungible as a source of funding for variation margin, we introduce a simulation/regression scheme for a class of anticipated BSDEs, where the coefficient entails a conditional expected shortfall of the martingale part of the solution. The scheme is explicit in time and uses neural network least-squares and quantile regressions for the embedded conditional expectations and expected shortfall computations. An a posteriori Monte Carlo validation procedure allows assessing the regression error of the scheme at each time step. The superiority of this scheme with respect to Picard iterations is illustrated in a high-dimensional and hybrid market/default risks XVA use-case.

翻译：受资本被视为可用于补充变动保证金资金来源的现实情形下的交叉估值调整（XVA）方程的启发，我们针对一类前瞻型倒向随机微分方程引入了一种模拟/回归方法。该方程的系数包含解的马丁格尔部分的条件期望损失。该方法在时间上是显式的，并采用神经网络最小二乘和分位数回归来处理嵌入的条件期望和期望损失计算。一个后验蒙特卡洛验证过程允许在每个时间步评估该方法的回归误差。在高维且混合市场/违约风险的XVA用例中，展示了该方法相对于Picard迭代的优越性。