NDLI: Phase-type Approximations to Finite-time Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models

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Phase-type Approximations to Finite-time Ruin Probabilities in the Sparre-Andersen and Stationary Renewal Risk Models

Content Provider	Scilit
Author	Stanford, D. A. Avram, F. Badescu, A. L. Breuer, L. Soares, A. Da Silva Latouche, G.
Copyright Year	2005
Description	The present paper extends the “Erlangization” idea introduced by Asmussen, Avram, and Usabel (2002) to the Sparre-Andersen and stationary renewal risk models. Erlangization 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.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/55226B0FAE9CCB981784DDC4EBFB9356/S0515036100014094a.pdf/div-class-title-phase-type-approximations-to-finite-time-ruin-probabilities-in-the-sparre-andersen-and-stationary-renewal-risk-models-div.pdf
Ending Page	144
Page Count	14
Starting Page	131
ISSN	05150361
e-ISSN	17831350
DOI	10.1017/s0515036100014094
Journal	ASTIN Bulletin
Issue Number	1
Volume Number	35
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	2005-05-01
Access Restriction	Open
Subject Keyword	ASTIN Bulletin Automotive Engineering andersen Model Ladder Height Maximal Aggregate Loss Deficit At Ruin type Distribution
Content Type	Text
Resource Type	Article
Subject	Finance Accounting Economics and Econometrics

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