Affine Point Processes: Approximation and Efficient Simulation

• 成果类型: Article
• 署名作者: Zhang, Xiaowei; Blanchet, Jose; Giesecke, Kay; Glynn, Peter W.
• 署名单位: Hong Kong University of Science & Technology; Columbia University; Stanford University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0696
• 发表日期: 2015
• 页码: 797-819
• 关键词: large deviations; hawkes processes; continuous-time; LIMIT-THEOREMS

摘要

We establish a central limit theorem and a large deviations principle for affine point processes, which are stochastic models of correlated event timing widely used in finance and economics. These limit results generate closed-form approximations to the distribution of an affine point process. They also facilitate the construction of an asymptotically optimal importance sampling estimator of tail probabilities. Numerical tests illustrate our results.