Exact Simulation of Point Processes with Stochastic Intensities

• 成果类型: Article
• 署名作者: Giesecke, K.; Kakavand, H.; Mousavi, M.
• 署名单位: Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1110.0962
• 发表日期: 2011
• 页码: 1233-1245
• 关键词: jump; DIFFUSIONS; models; time

摘要

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.