In this article we mainly extend to a multi-currency setting some previous works in the literature concerning total value adjustments in a single currency framework. The motivation comes from the fact that financial institutions operate in global markets, so that the financial derivatives in their portfolios involve different currencies. More precisely, in this multi-currency setting we pose the PDE formulations for pricing the total adjustment and the financial derivative with counterparty risk. Moreover, we also formulate the problem in terms of expectations, which allows the use of suitable Monte Carlo techniques that overcome the curse of dimensionality associated to the numerical solution of PDE formulation, when a high number of stochastic factors are involved. Finally, we present some examples to illustrate the performance of the formulations and the proposed numerical techniques.

在本文中，我们主要扩展到多币种设置，之前文献中关于单一货币框架中的总价值调整的一些工作。动机来自于金融机构在全球市场运作，因此其投资组合中的金融衍生品涉及不同的货币。更准确地说，在这种多货币环境中，我们提出了 PDE 公式，用于对总调整和具有交易对手风险的金融衍生工具进行定价。此外，我们还根据期望来制定问题，当涉及大量随机因素时，这允许使用合适的蒙特卡罗技术来克服与 PDE 公式的数值解相关的维数灾难。最后，