Uniform estimates for ruinprobabilities in the renewal risk model with upper-tail independentclaims and premiums

Yinghua Dong; Yuebao Wang

doi:10.3934/jimo.2011.7.849

Article Contents

2011, Volume 7, Issue 4: 849-874. Doi: 10.3934/jimo.2011.7.849

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Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiums

Yinghua Dong^1, and
Yuebao Wang^1,

1.
Department of Mathematics, Soochow University, Suzhou, 215006

Received: April 30, 2010

Revised: April 30, 2011

Published: September 2011

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Abstract

In this paper, we discuss a nonstandard renewal risk model, where the price process of the investment portfolio is modelled as a geometric Lévy process, the claim sizes and premium sizes form sequences of identically distributed and upper-tail independent random variables, respectively, the claim size and its corresponding inter-claim time satisfy a certain dependence structure described via a conditional tail probability of the claim size given the inter-claim time before the claim occurs, and there is a similar dependence structure between the premium size and the inter-arrival time before the premium is paid. When the claim-size distribution belongs to the extended-regular-varying class, we obtain a uniform tail asymptotics for stochastically discounted aggregate claims. Furthermore, assuming that the tail of the premium-size distribution is lighter than that of the claim-size distribution, the uniform estimates for the finite- and infinite-time ruin probabilities are presented respectively.

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Mathematics Subject Classification: Primary: 91B30; Secondary: 60G70, 91B28.

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