Abstract This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind that have recently been studied for partial integro-differential equations (PIDEs) in [3] . Each of these schemes conveniently treats the nonlocal integral part in an explicit manner. Their adaptation to PIDCPs is achieved through a combination with the Ikonen–Toivanen splitting technique [14] as well as with the penalty method [32] . The convergence behaviour and relative performance of the acquired eight operator splitting methods is investigated in extensive numerical experiments for American put-on-the-min and put-on-the-average options.

中文翻译：

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二资产默顿跳跃扩散模型下美式期权的算子拆分方案

摘要 本文讨论了二维偏积分微分互补问题（PIDCP）的有效数值解，该问题在二资产默顿跳跃扩散模型下适用于美式期权的价值。我们考虑了隐式显式 (IMEX) 和交替方向隐式 (ADI) 类型的各种算子分裂方案的适应，这些方案最近在 [3] 中研究了偏积分微分方程 (PIDE)。这些方案中的每一个都以明确的方式方便地处理非局部积分部分。它们对 PIDCP 的适应是通过结合 Ikonen-Toivanen 分裂技术 [14] 以及惩罚方法 [32] 来实现的。