Exact asymptotics of ruin probabilities with linear Hawkes arrivals

TL;DR

This paper derives precise asymptotic estimates for ruin probabilities in risk processes driven by linear Hawkes process arrivals, considering both light-tailed and heavy-tailed claim sizes, using advanced probabilistic techniques.

Contribution

It provides the first detailed asymptotic analysis of ruin probabilities with Hawkes process arrivals, extending classical risk models to self-exciting point processes.

Findings

Exact asymptotics for ruin probabilities established

Bounds derived for both light-tailed and heavy-tailed claims

Methodology based on one big jump, change of measure, and renewal theory

Abstract

In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is based on the principle of one big jump, exponential change of measure, and renewal arguments.