A backward construction and simulation of correlated Poisson processes

In this paper, we consider a generalisation of the backward simulation method of Duch et al. [New approaches to operational risk modeling. IBM J Res Develop. 2014; 58: 1-9] to build bivariate Poisson processes with flexible time correlation structures, and to simulate the arrival times of the processes. The proposed backward construction approach uses the Marshall- Olkin bivariate binomial distribution for the conditional law and some well-known families of bivariate copulas for the joint success probability in lieu of the typical conditional independence assumption. The resulting bivariate Poisson process can exhibit various time correlation structures which are commonly observed in real data.