Risk Theory in a Finite Customer-Pool Setting

Markov Processes And Related Fields, pp. 165–204

Abstract

This paper investigates an insurance model with a finite number of major clients and a large number of small clients, where the dynamics of the latter group are modeled by a spectrally positive Levy process. We begin by analyzing this general model, in which the inter-arrival times´ are exponentially distributed (though not identically), and derive the closed-form Laplace transform of the ruin probability. Next, we examine a simplified version of the model involving only the major clients, and explore the tail asymptotics of the ruin probability, focusing on the cases where the claim sizes follow phase-type or regularly varying distributions. Finally, we derive the distribution of the overshoot over an exponentially distributed initial reserve, expressed in terms of its Laplace-Stieltjes transform.

Authors 2

1. Michel Mandjes

   University of Amsterdam

   Affiliation as printed

   University of Amsterdam

   University of Amsterdam, Spui 21, Amsterdam, 1018 WB, Netherlands

2. Daniël Rutgers corresponding Aachen

   Leiden University

   Affiliation as printed

   Leiden University

   Leiden University, Postbus 9500, Leiden, 2300 RA, Netherlands