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Title: Multivariate frequency-severity regression models in insurance Authors:  Edward Frees - University of Wisconsin-Madison (United States)
Gee Lee - University of Wisconsin-Madison (United States)
Lu Yang - University of Amsterdam (Netherlands) [presenting]
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. We will synthesize and extend 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. The focus is 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. 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.