# Correlated Multivariate Poisson Processes and Extreme Measures

## TL;DR

This paper explores the modeling of multivariate Poisson processes using backward simulation and investigates their connection to extreme measures that describe their joint distribution at the end of the simulation period.

## Contribution

It introduces a backward simulation approach for multivariate Poisson processes and analyzes the relationship to extreme measures, advancing understanding of their joint distributions.

## Key findings

- Backward simulation effectively models multivariate Poisson processes.
- Extreme measures characterize joint distributions at terminal time.
- The approach enhances simulation accuracy for applications in finance and insurance.

## Abstract

Multivariate Poisson processes have many important applications in Insurance, Finance, and many other areas of Applied Probability. In this paper we study the backward simulation approach to modelling multivariate Poisson processes and analyze the connection to the extreme measures describing the joint distribution of the processes at the terminal simulation time.