Exact Simulation of Point Processes with Stochastic Intensities

31 Pages Posted: 15 Feb 2010 Last revised: 13 Sep 2010

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Management Science & Engineering

Hossein Kakavand

Stanford University

Mohammad Mousavi

Stanford University - Management Science & Engineering

Date Written: 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.

Keywords: Point Process, Stochastic Intensity, Filtering, Filtration

Suggested Citation

Giesecke, Kay and Kakavand, Hossein and Mousavi, Mohammad, Exact Simulation of Point Processes with Stochastic Intensities (September 9, 2010). Available at SSRN: https://ssrn.com/abstract=1551647 or http://dx.doi.org/10.2139/ssrn.1551647

Kay Giesecke (Contact Author)

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://www.stanford.edu/~giesecke/

Hossein Kakavand

Stanford University ( email )

Stanford, CA 94305
United States

Mohammad Mousavi

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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