Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims

2018/01/31 by Zailei Cheng, Youngsoo Seol
Economics, Econometrics and Finance · Mathematics · #math.PR #q-fin.RM

paper · pdf · doi:10.1007/s11009-019-09722-8

published as Methodology and Computing in Applied Probability 2019 · 21 pages,3 figures. arXiv admin note: text overlap with arXiv:1607.06624, arXiv:1702.05852, arXiv:1309.7621 by other authors

arxiv created 2019/08/21 · arxiv updated 2019/08/22

Abstract

We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size is small. The main goal of the article is to establish a diffusion approximation by verifying a functional central limit theorem and to compute the ruin probability in finite-time horizon. Numerical results will also be given.

Citations

• Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
• Some asymptotic results for nonlinear Hawkes processes
• Gaussian risk models with financial constraints