We study the principal component analysis based approach introduced by Reisinger & Wittum (2007) and the comonotonic approach considered by Hanbali & Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

中文翻译：

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通过偏微分互补问题对美式篮子期权进行数值估值

我们研究了 Reisinger & Wittum (2007) 引入的基于主成分分析的方法和 Hanbali & Linders (2019) 考虑的共调方法，用于通过多维偏微分互补问题 (PDCP) 逼近美国篮子期权的价值。两种近似方法都只需要解决有限数量的低维 PDCP。大量的数值实验证明，它们定义了彼此接近的近似值。接下来，提出了相关 PDCP 的有效离散化，从而导致有利的收敛行为。