PEETERS ONLINE JOURNALS
Peeters Online Bibliographies
Peeters Publishers
this issue
  previous article in this issuenext article in this issue  

Document Details :

Title: Phase-Type Approximations to Finite Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models
Author(s): STANFORD, D.A. , AVRAM, F. , BADESCU, A.L. , BREUER, L. , DA SILVA SOARES, A. , LATOUCHE, G.
Journal: ASTIN Bulletin
Volume: 35    Issue: 1   Date: May 2005   
Pages: 131-144
DOI: 10.2143/AST.35.1.583169

Abstract :
The present paper extends the 'Erlangization' idea introduced by Asmussen, Avram and Usabel (2002) to the Sparre-Andersen and stationary renewal risk models. Erangization yields an asymptotically-exact method for calculating finite time ruin probabilities with phase-type claim amounts. The method is based on finding the probability of ruin prior to a phase-type random horizon, independent of the risk process. When the horizon follows an Erlang-l distribution, the method provides a sequence of approximations that converges to the true finite-time ruin probability as l increases. Furthermore, the random horizon is easier to work with, so that very accurate probabilities of ruin are obtained with comparatively little computational effort. An additional section determines the phase-type form of the deficit at ruin in both models. Our work exploits the relationship to fluid queues to provide effective computational algorithms for the determination of these quantities, as demonstrated by the numerical examples.

3.234.211.61.