On corrected phase-type approximations of the time value of ruin with heavy tails

Geiger Daniel J. () and Adekpedjou Akim ()
Additional contact information
Geiger Daniel J.: Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W 12th St, Rolla, MO 65409, USA
Adekpedjou Akim: Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W 12th St, Rolla, MO 65409, USA

Statistics & Risk Modeling, 2019, vol. 36, issue 1-4, 57-75

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.

Keywords: Corrected phase-type approximations; time value of ruin; Gerber–Shiu expected discounted penalty functions; heavy-tailed claim size distributions; tail asymptotics; dependent risk models (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/strm-2019-0009 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:36:y:2019:i:1-4:p:57-75:n:4

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1515/strm-2019-0009

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().