Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence

Qihe Tang and Li Wei

Insurance: Mathematics and Economics, 2010, vol. 46, issue 1, 19-31

Abstract: We study the asymptotic behavior of the Gerber-Shiu expected discounted penalty function in the renewal risk model. Under the assumption that the claim-size distribution has a convolution-equivalent density function, which allows both heavy-tailed and light-tailed cases, we establish some asymptotic formulas for the Gerber-Shiu function with a fairly general penalty function. These formulas become completely transparent in the compound Poisson risk model or for certain choices of the penalty function in the renewal risk model. A by-product of this work is an extension of the Wiener-Hopf factorization to include the times of ascending and descending ladders in the continuous-time renewal risk model.

Keywords: Asymptotics; Convolution; equivalence; Duality; principle; Gerber-Shiu; function; Renewal; risk; model; Wiener-Hopf; factorization (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:46:y:2010:i:1:p:19-31

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