Backward Simulation of Multivariate Mixed Poisson Processes

TL;DR

This paper extends a backward simulation method to generate correlated multivariate mixed Poisson processes, enabling efficient sampling with a wide range of correlations, including extreme cases, useful in various applied fields.

Contribution

The paper introduces an extension of the backward simulation approach to multivariate mixed Poisson processes, allowing for flexible correlation modeling and efficient path generation.

Findings

Able to simulate processes with extreme positive and negative correlations

Provides a simple and efficient method for generating sample paths

Extends previous work to include mixed Poisson processes

Abstract

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.