The joint distribution of the Parisian ruin time and the number of claims until Parisian ruin in the classical risk model

TL;DR

This paper introduces an iterative algorithm to compute the joint distribution of Parisian ruin time and claim count in the classical risk model, with examples for exponential claim sizes.

Contribution

It presents a novel iterative method for calculating the joint distribution of Parisian ruin time and claim number, enhancing analytical tools in risk theory.

Findings

Algorithm successfully computes joint distributions

Applicable to exponential claim size distributions

Provides practical examples demonstrating effectiveness

Abstract

In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is exponentially distributed.