Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claims

TL;DR

This paper derives ruin probability asymptotics for risk processes with subexponential claims and non-stationary, dependent arrival processes satisfying large deviation principles, including examples like Hawkes and Cox processes.

Contribution

It extends ruin probability analysis to non-stationary, dependent arrival processes with subexponential claims, providing new asymptotic results and examples.

Findings

Asymptotic ruin probabilities derived for non-stationary processes

Includes examples with Hawkes, Cox, and self-correcting processes

Provides aggregate claims results for these processes

Abstract

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give three examples of non-stationary and non-renewal point processes: Hawkes process, Cox process with shot noise intensity and self-correcting point process. We also show some aggregate claims results for these three examples.