Point processes with stochastic arrival intensities are ubiquitous in many areas, including finance, insurance, reliability, health care, and queuing. They can be simulated from a Poisson process by time scaling with the cumulative intensity. The paths of the cumulative intensity are often generated with a discretization method. However, discretization introduces bias into the simulation results. The magnitude of the bias is difficult to quantify. This paper develops a sampling method that eliminates the need to discretize the cumulative intensity. The method is based on a projection argument and leads to unbiased simulation estimators. It is exemplified for a point process whose intensity is a function of a jump-diffusion process and the point process itself. In this setting, the method facilitates the exact sampling of both the point process and the driving jump-diffusion process. Numerical experiments demonstrate the effectiveness of the method. Subject classifications: point process; intensity projection; filtering; exact sampling. Area of review: Simulation. History: Received March 2010; revisions received June 2010, September 2010; accepted September 2010. © 2011 INFORMS.
CITATION STYLE
Giesecke, K., Kakavand, H., & Mousavi, M. (2011). Exact simulation of point processes with stochastic intensities. Operations Research, 59(5), 1233–1245. https://doi.org/10.1287/opre.1110.0962
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