"On Corrected Phase-Type Approximations of the Time Value of Ruin with " by Daniel J. Geiger and Akim Adekpedjou
 

On Corrected Phase-Type Approximations of the Time Value of Ruin with Heavy Tails

Abstract

We approximate Gerber-Shiu functions with heavy-tailed claims in a recently introduced risk model having both interclaim times and premiums depending on the claim sizes. We apply a technique known as "corrected phase-type approximations". This results in adding a correction term to the Gerber-Shiu function with phase-type claim sizes. The correction term contains the heavy-tailed behavior at most once per convolution and captures the tail behavior of the true Gerber-Shiu function. We make the tail behavior specific in the classical case of one class of risk insured. After illustrating a use of such approximations, we study numerically the approximations' relative errors for some specific penalty functions and claims distributions.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Corrected Phase-Type Approximations; Dependent Risk Models; Gerber-Shiu Expected Discounted Penalty Functions; Heavy-Tailed Claim Size Distributions; Tail Asymptotics; Time Value of Ruin

International Standard Serial Number (ISSN)

2193-1402

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 De Gruyter, All rights reserved.

Publication Date

01 Dec 2019

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