Predictive Modeling of Multi-Peril Homeowners Insurance

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.