Dependent Multi-Peril Ratemaking Models

Abstract

This paper considers insurance claims that are available by cause of loss, or peril. Using this multi-peril information, we investigate multivariate frequency and severity models, emphasizing alternative dependency structures. Although dependency models may be used for many risk management strategies, we focus on ratemaking. Motivation for this research comes from homeowners insurance and so, for the frequency portion, we consider binary response models. Specifically, we examine several multivariate binary regression models that have appeared in the biomedical literature, focusing on a dependence ratio model. For multivariate severity, we use Gaussian copulas to represent dependencies among gamma regressions. We calibrate competing models based on a representative sample of over 400, 000 records and validate them using a held-out sample of over 350, 000 records. We find that methods that allow for cross-dependencies among perils provide important economic value in pricing.