Parisian Ruin Probability Of An Integrated Gaussian Risk Model

TL;DR

This paper analyzes the Parisian ruin probability for an integrated Gaussian risk model, showing asymptotic equivalence with classical ruin probability and providing an approximation for the ruin time.

Contribution

It establishes the asymptotic equivalence of Parisian and classical ruin probabilities for integrated Gaussian processes and derives a ruin time approximation.

Findings

Parisian and classical ruin probabilities are asymptotically the same on the log-scale.

The probabilities are also asymptotically equivalent for small intervals below zero.

An approximation for the conditional ruin time is derived.

Abstract

In this paper we investigate the Parisian ruin probability for an integrated Gaussian process. Under certain assumptions, we find the Parisian ruin probability and the classical ruin probability are on the log-scale asymptotically the same. Moreover, for any small interval required by the risk process staying below level zero, the Parisian ruin probability and the classical one are the same also in the premise asymptotic behavior. Furthermore, we derive an approximation of the conditional ruin time.