Insurance pricing with hierarchically structured data: An illustration with a workers' compensation insurance portfolio

TL;DR

This paper explores advanced hierarchical modeling techniques for insurance pricing, demonstrating improved predictive accuracy and risk differentiation in workers' compensation insurance by incorporating structured risk factors and distributional assumptions.

Contribution

It introduces a data-driven approach to hierarchical insurance pricing models, comparing credibility and mixed models, and highlights the benefits of Tweedie distribution for loss cost prediction.

Findings

Hierarchical models improve predictive performance.

Incorporating contract-specific risk factors enhances risk differentiation.

Tweedie distribution effectively models loss costs.

Abstract

Actuaries use predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. State-of-the-art statistical and machine learning methods are not well equipped to handle hierarchically structured risk factors with a large number of levels. In this paper, we demonstrate the data-driven construction of an insurance pricing model when hierarchically structured risk factors, contract-specific as well as externally collected risk factors are available. We examine the pricing of a workers' compensation insurance product with a hierarchical credibility model (Jewell, 1975), Ohlsson's combination of a generalized linear and a hierarchical credibility model (Ohlsson, 2008) and mixed models. We compare the predictive performance of these models and evaluate the effect of the distributional assumption on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. For our case-study the Tweedie distribution is well suited to model and predict the loss cost on a contract. Moreover, incorporating contract-specific risk factors in the model improves the predictive performance and the risk differentiation in our workers' compensation insurance portfolio.