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Frees, Edward W., Glenn Meyers, and A. David Cummings. 2012. “Predictive Modeling of Multi-Peril Homeowners Insurance.” Variance 6 (1): 11–31.
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  • Figure 1. Single versus multi-peril frequency-severity scores. This graph is based on a 1 in 100 random sample of size 3,594. The correlation coefficient is only 79.4%; the figure shows substantial variation between the two sets of scores.
  • Figure 2. Average relativities and loss ratios by groups of scores. Each panel displays a linear relationship. The variability about the relationship increases as the number of bins increases.
  • Figure 3. Comparison of single and multi-peril frequency-severity loss ratios. The deviations from IND_FreqSev and SP_FreqSev are comparable and it is difficult to say which score is uniformly better.
  • Figure 4. Comparison of loss ratios from several scoring methods. The left panel compares the independence to an instrumental variable frequency-severity approach; the latter is clearly preferred to the former. The right panel compares the independence frequency-severity approach to the single peril pure premium (Tweedie) method. These two measures perform about the same for most of the data.

Abstract

Predictive models are used by insurers for underwriting and ratemaking in personal lines insurance. Focusing on homeowners insurance, this paper examines many predictive generalized linear models, including those for pure premium (Tweedie), frequency (logistic) and severity (gamma). We compare predictions from models based on a single peril, or cause of loss, to those based on multiple perils. For multi-peril models, we introduce an instrumental variable approach to account for dependencies among perils. We calibrate these models using a database of detailed individual policyholder experience. To evaluate these many alternatives, we emphasize out-of-sample model comparisons. We utilize Gini indices for global comparisons of models and, for local comparisons, introduce nonparametric regression techniques. We find that using several different comparison approaches can help the actuary critically evaluate the effectiveness of alternative prediction procedures.