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

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

Dimitrios G. Konstantinides, Kai W. Ng, and Qihe Tang

Source: J. Appl. Probab. Volume 47, Number 2 (2010), 323-334.

Abstract

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.

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Primary Subjects: 91B30

Secondary Subjects: 60G70, 60K05

Keywords: Absolute ruin; asymptotics; constant force of interest; convolution equivalence; heavy tail; renewal risk model

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Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784894
Digital Object Identifier: doi:10.1239/jap/1276784894
Zentralblatt MATH identifier: 05758472
Mathematical Reviews number (MathSciNet): MR2668491

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