2022/11/30 by Raviar Karim, Roger J. A. Laeven, Karim, Raviar S. +3 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Probability and Risk Models #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2211.16848
openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we establish a large deviations principle for a multivariate compound process induced by a multivariate Hawkes process with random marks. Our proof hinges on showing essential smoothness of the limiting cumulant of the multivariate compound process, resolving the inherent complication that this cumulant is implicitly characterized through a fixed-point representation. We employ the large deviations principle to derive logarithmic asymptotic results on the marginal ruin probabilities of the associated multivariate risk process. We also show how to conduct rare event simulation in this multivariate setting using importance sampling and prove the asymptotic efficiency of our importance sampling based estimator. The paper is concluded with a systematic assessment of the performance of our rare event simulation procedure.