Exact Simulation of Point Processes with Stochastic Intensities

K. Giesecke (), H. Kakavand () and M. Mousavi ()
Additional contact information
K. Giesecke: Department of Management Science and Engineering, Stanford University, Stanford, California 94305
H. Kakavand: The Perot Group
M. Mousavi: Department of Management Science and Engineering, Stanford University, Stanford, California 94305

Operations Research, 2011, vol. 59, issue 5, 1233-1245

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; intensity projection; filtering; exact sampling (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (14)

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