Next Article in Journal
Valuation of Large Variable Annuity Portfolios Using Linear Models with Interactions
Previous Article in Journal
Association Rules for Understanding Policyholder Lapses
Article Menu

Export Article

Open AccessArticle
Risks 2018, 6(3), 70; https://doi.org/10.3390/risks6030070

Log-Normal or Over-Dispersed Poisson?

Department of Economics, University of Oxford & Oriel College, Oxford OX1 4EW, UK
Received: 18 June 2018 / Revised: 5 July 2018 / Accepted: 6 July 2018 / Published: 9 July 2018
Full-Text   |   PDF [986 KB, uploaded 10 July 2018]   |  

Abstract

Although both over-dispersed Poisson and log-normal chain-ladder models are popular in claim reserving, it is not obvious when to choose which model. Yet, the two models are obviously different. While the over-dispersed Poisson model imposes the variance to mean ratio to be common across the array, the log-normal model assumes the same for the standard deviation to mean ratio. Leveraging this insight, we propose a test that has the power to distinguish between the two models. The theory is asymptotic, but it does not build on a large size of the array and, instead, makes use of information accumulating within the cells. The test has a non-standard asymptotic distribution; however, saddle point approximations are available. We show in a simulation study that these approximations are accurate and that the test performs well in finite samples and has high power. View Full-Text
Keywords: non-nested testing; encompassing; chain-ladder non-nested testing; encompassing; chain-ladder
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Harnau, J. Log-Normal or Over-Dispersed Poisson? Risks 2018, 6, 70.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top