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The probabilities of absolute ruin in the renewal risk model with constant force of interest

Part of: Stochastic processes Special processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Dimitrios G. Konstantinides ,
Kai W. Ng  and
Qihe Tang
Dimitrios G. Konstantinides*
Affiliation:
University of the Aegean
Kai W. Ng*
Affiliation:
The University of Hong Kong
Qihe Tang*
Affiliation:
The University of Iowa
*
∗Postal address: Department of Statistics and Actuarial - Financial Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece. Email address: [email protected]
∗∗Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: [email protected]
∗∗∗Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: [email protected]
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Abstract

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In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.

Keywords

Absolute ruinasymptoticsconstant force of interestconvolution equivalenceheavy tailrenewal risk model

MSC classification

Secondary: 91B30: Risk theory, insurance 60G70: Extreme value theory; extremal processes 60K05: Renewal theory
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 323 - 334
Copyright
Copyright © Applied Probability Trust 2010 

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