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

TL;DR

This paper develops a diffusion approximation for a risk model with non-stationary Hawkes process claims, providing insights into ruin probabilities under large premium and claim arrival intensities.

Contribution

It introduces a novel diffusion approximation for a risk process with non-stationary Hawkes arrivals, extending classical models to more complex, self-exciting claim processes.

Findings

Established a functional central limit theorem for the model

Derived finite-time ruin probability estimates

Provided numerical illustrations of the approximation

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.