A credibility-based Erlang mixture model for pricing crop reinsurance

Journal article

Lysa Porth; Wenjun Zhu; Ken Seng Tan

Agricultural Finance Review · 2014-07-01 · Volume 74 · Issue 2 · pp. 162-187
DOI: 10.1108/afr-04-2014-0006 · Download citation (BibTeX)

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Abstract

This paper comprehensively examines the ratemaking process, including reviews of different detrending methods and the generating process of the historical loss cost ratio's (LCR's, which is defined as the ratio of indemnities to liabilities). A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR. In the empirical analysis, 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. 

Keywords: Erlang mixture; Credibiilty; EM Algorithm; Reinsurance Ratemaking

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