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Multivariate Frequency-Severity Regression Models in Insurance

School of Business, University of Wisconsin-Madison, 975 University Avenue, Madison, WI 53706, USA
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
PDF [1223 KB, uploaded 25 February 2016]


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

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

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