Incorporating Frequency-Severity Dependence into Collective Risk Models

• Activity Number: 566 - Analytics in Insurance Operations: Novel Statistical Methods and Applications
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Casualty Actuarial Society
• Author(s): Zifeng Zhao* and Peng Shi
• Companies: University of Notre Dame and University of Wisconsin-Madison
• Keywords: Aggregate insurance claims; Compound distributions; Copula regression; Incomplete data; Two-part models

Abstract

In this article, we introduce a novel regression model for compound distributions that allows for arbitrary dependence between the primary (frequency) and the secondary (severity) variables. Relaxing the independence assumption in the standard compound distribution, we propose a novel copula-linked compound distribution that uses a parametric copula to accommodate the association between the frequency and severity components. The resulting copula regression framework is flexible enough to nest several commonly used approaches as special cases, including the hurdle model, the selection model, and the frequency-severity model, among others. We further show that the new model can be easily modified to account for incomplete data due to censoring or truncation. Because of the parametric nature, likelihood-based approaches are proposed for estimation, inference, and diagnostics. In the application, we consider the collective risk model for aggregating losses in an insurance system.