The simulation of correlated multivariate Poisson processes with negative correlation between their components has many important applications in Finance, Insurance, Geophysics, and many other areas of applied probability. Introduced in our earlier work, the Backward Simulation (BS) approach to the simulation of correlated multivariate Poisson processes is able to capture a wide range of correlation, including extreme positive and extreme negative correlation, that is not possible with other approaches such as the forward simulation approach. Moreover, the BS approach enables simple and efficient generation of sample paths of correlated multivariate Poisson processes. In this work, we extend the BS approach to multivariate mixed Poisson processes.

其分量之间呈负相关的相关多元泊松过程的模拟在金融、保险、地球物理学和许多其他应用概率领域有许多重要应用。在我们早期的工作中介绍过，用于模拟相关多元泊松过程的后向模拟 (BS) 方法能够捕获广泛的相关性，包括极端正相关和极端负相关，这是其他方法（如前向相关）无法实现的模拟方法。此外，BS 方法能够简单有效地生成相关多元泊松过程的样本路径。在这项工作中，我们将 BS 方法扩展到多元混合泊松过程。