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A credibility-based Erlang mixture model for pricing crop reinsurance

Lysa Porth (Warren Centre for Actuarial Studies and Research and Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada)
Wenjun Zhu (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada)
Ken Seng Tan (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada and China Institute of Actuarial Science, Central University of Finance and Economics, Beijing, China)

Agricultural Finance Review

ISSN: 0002-1466

Article publication date: 1 July 2014



The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework.


The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixture distribution is proposed. A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR, and information from the observed data of the individual region/province is integrated with the collective experience of the entire crop reinsurance program in Canada.


A comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR's is more conservative, and provides a more scientific approach to enhance the reinsurance pricing.

Research limitations/implications

Credibility models are in the early stages of application in the area of agriculture insurance, therefore, the credibility models presented in this paper could be verified with data from other geographical regions.

Practical implications

The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks.


This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Bühlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.



Zhu acknowledges funding support from the Society of Actuaries Hickman Scholar Program and the China Scholarship Council. Tan acknowledges research funding from the Natural Sciences and Engineering Research Council of Canada and the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (No.13JJD790041). All three authors are grateful to Joshua Woodard for his constructive comments and Neil Hamilton and Doug Wilcox from Manitoba Agriculture Services Corporation (MASC) for their assistance in obtaining the data.


Porth, L., Zhu, W. and Seng Tan, K. (2014), "A credibility-based Erlang mixture model for pricing crop reinsurance", Agricultural Finance Review, Vol. 74 No. 2, pp. 162-187.



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