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Risks 2016, 4(1), 4; doi:10.3390/risks4010004

Multivariate Frequency-Severity Regression Models in Insurance

1
School of Business, University of Wisconsin-Madison, 975 University Avenue, Madison, WI 53706, USA
2
Department of Statistics, University of Wisconsin-Madison, 1300 University Avenue, Madison, WI 53706, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Guillén
Received: 16 November 2015 / Accepted: 15 February 2016 / Published: 25 February 2016
View Full-Text   |   Download PDF [1223 KB, uploaded 25 February 2016]   |  

Abstract

In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors’ equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line. View Full-Text
Keywords: tweedie distribution; copula regression; government insurance; dependency modeling; inflated count model tweedie distribution; copula regression; government insurance; dependency modeling; inflated count model
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).

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MDPI and ACS Style

Frees, E.W.; Lee, G.; Yang, L. Multivariate Frequency-Severity Regression Models in Insurance. Risks 2016, 4, 4.

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