On Corrected Phase-Type Approximations of the Time Value of Ruin with Heavy Tails
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.
D. J. Geiger and A. Adekpedjou, "On Corrected Phase-Type Approximations of the Time Value of Ruin with Heavy Tails," Statistics and Risk Modeling, vol. 36, no. 1-4, pp. 57 - 75, De Gruyter, Dec 2019.
The definitive version is available at https://doi.org/10.1515/strm-2019-0009
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)
Article - Journal
© 2019 De Gruyter, All rights reserved.
01 Dec 2019