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Algorithmic Analysis of the Sparre Andersen Model in Discrete Time

Published online by Cambridge University Press:  17 April 2015

Attahiru Sule Alfa  and
Steve Drekic
Attahiru Sule Alfa
Affiliation:
Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg, Manitoba, Canada R3T 5V6, E-mail: alfa@ee.umanitoba.ca
Steve Drekic
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Ave. West, Waterloo, Ontario, Canada N2L 3G1, E-mail: sdrekic@math.uwaterloo.ca
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Abstract

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In this paper, we show that the delayed Sparre Andersen insurance risk model in discrete time can be analyzed as a doubly infinite Markov chain. We then describe how matrix analytic methods can be used to establish a computational procedure for calculating the probability distributions associated with fundamental ruin-related quantities of interest, such as the time of ruin, the surplus immediately prior to ruin, and the deficit at ruin. Special cases of the model, namely the ordinary and stationary Sparre Andersen models, are considered in several numerical examples.

Keywords

Sparre Andersen modeldiscrete timematrix analytic methodstime of ruinsurplus immediately prior to ruindeficit at ruin
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 293 - 317
Copyright
Copyright © ASTIN Bulletin 2007

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