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Exact Simulation of Point Processes with Stochastic Intensities

by Kay Giesecke of Stanford University,
Hossein Kakavand of the Perot Group, and
Mohammad Mousavi of Stanford University

September 9, 2010

Abstract: 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.

Previously titled: Simulating Point Processes by Intensity Projection

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