Stanford, David and Avram, Florin and Badescu, Andrei and Breuer, Lothar (2005) Phase-type approximations to finite-time ruin probabilities in the Sparre Andersen and stationary renewal risk models. ASTIN Bulletin, 35 (1). pp. 131-144. ISSN 0515-0361 .
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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.
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Lothar Breuer|
|Date Deposited:||18 Nov 2008 14:53|
|Last Modified:||01 May 2009 15:45|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/12995 (The current URI for this page, for reference purposes)|
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