This paper investigates a numerical method for solving fractional partial integro-differential equations (FPIDEs) arising in American Contingent Claims, which follow finite moment log-stable process (FMLS) with jump diffusion and regime switching. Mathematically, the prices of American Contingent Claims satisfy a system of problems with free-boundary values, where is the number of regimes of the market. In addition, an optimal exercise boundary is needed to setup with each regime. Therefore, a fully implicit scheme based on the penalty term is arranged. In the end, numerical examples are carried out to verify the obtained theoretical results, and the impacts of state variables in our model on the optimal exercise boundary of American Contingent Claims are analyzed.

中文翻译：

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FMLS模型下美国或然索赔中产生的PIDE系统的跳跃扩散和状态转换过程的数值方法

本文研究了一种求解美国或然债权中出现的分数式偏积分微分方程 (FPIDE) 的数值方法，该方程遵循有限矩对数稳定过程 (FMLS)，具有跳跃扩散和状态切换。在数学上，美国或有债权的价格满足具有自由边界价值的问题系统，其中是市场制度的数量。此外，每个制度都需要一个最佳的运动边界来设置。因此，安排了一个基于惩罚项的全隐式方案。最后通过数值算例对所得理论结果进行验证，并分析了模型中状态变量对美国或然债权最优行使边界的影响。