Risky Loss Distributions and Modeling the Loss Reserve Payout Tail

34 Pages Posted: 1 Nov 2004

See all articles by J David Cummins

J David Cummins

Temple University - Risk Management & Insurance & Actuarial Science

James McDonald

Brigham Young University

Craig B. Merrill

Brigham Young University; Wharton Financial Institutions Center

Date Written: October 12, 2004

Abstract

Although an extensive literature has developed on modeling the loss reserve runoff triangle, the estimation of severity distributions applicable to claims settled in specific cells of the runoff triangle has received little attention in the literature. This paper proposes the use of a very flexible probability density function, the generalized beta of the 2nd kind (GB2) to model severity distributions in the cells of the runoff triangle and illustrates the use of the GB2 based on a sample of nearly 500,000 products liability paid claims. The results show that the GB2 provides a significantly better fit to the severity data than conventional distributions such as the Weibull, Burr 12, and generalized gamma and that modeling severity by cell is important to avoid errors in estimating the riskiness of liability claims payments, especially at the longer lags.

Keywords: Loss distributions, loss reserves, generalized beta distribution, liability insurance

JEL Classification: C16, G22

Suggested Citation

Cummins, J. David and McDonald, James B. and Merrill, Craig B., Risky Loss Distributions and Modeling the Loss Reserve Payout Tail (October 12, 2004). Available at SSRN: https://ssrn.com/abstract=610603 or http://dx.doi.org/10.2139/ssrn.610603

J. David Cummins (Contact Author)

Temple University - Risk Management & Insurance & Actuarial Science ( email )

Fox School of Business and Management
1801 Liacouras Walk.
Philadelphia, PA 19122
United States
215-204-8468 (Phone)
215-204-4712 (Fax)

James B. McDonald

Brigham Young University ( email )

130 Faculty Office Bldg.
Provo, UT 84602-2363
United States
801-378-3463 (Phone)

Craig B. Merrill

Brigham Young University ( email )

Provo, UT 84602
United States
(801) 422-4782 (Phone)

Wharton Financial Institutions Center ( email )

2306 Steinberg Hall-Dietrich Hall
3620 Locust Walk
Philadelphia, PA 19104
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
263
Abstract Views
2,168
rank
128,815
PlumX Metrics