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

**Authors:** Bavo D. C. Campo, Katrien Antonio  
**arXiv:** [2206.15244](https://arxiv.org/abs/2206.15244)  
**Date:** 2022-06-30  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2206.15244v1/

## Key points

- The paper explores the use of predictive modeling techniques to assess loss costs 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.
- The paper demonstrates the construction of a data-driven insurance pricing model when hierarchically structured risk factors, both contract-specific and externally collected ones, are available.
- The study focuses on the pricing of a workers' compensation insurance product using three different models: hierarchical credibility model, Ohlsson's combination of a generalized linear and hierarchical credibility model, and mixed models.
- The authors compare the predictive performance of these models and evaluate the effect of distributional assumptions on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models.
- For their case-study, the Tweedie distribution is well suited to model and predict the loss cost on a contract.
- Incorporating contract-specific risk factors in the predictive model improves performance and allows for improved risk differentiation in their workers' compensation insurance portfolio.
- This paper provides valuable insights into how actuaries can effectively use predictive modeling techniques to assess loss costs on contracts while accounting for hierarchically structured risk factors.
- The findings have important implications for insurers looking to improve their pricing strategies and better manage risks associated with complex insurance products like workers' compensation.

## Summary

The paper "Insurance pricing with hierarchically structured data: An illustration with a workers' compensation insurance portfolio" explores the use of predictive modeling techniques to assess the loss cost on a contract as a function of observable risk characteristics. The authors note that 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. To address this issue, the paper demonstrates the construction of a data-driven insurance pricing model when hierarchically structured risk factors, both contract-specific and externally collected ones, are available. The study focuses on the pricing of a workers' compensation insurance product using three different models: hierarchical credibility model (Jewell, 1975), Ohlsson's combination of a generalized linear and hierarchical credibility model (Ohlsson, 2008), and mixed models. The authors compare the predictive performance of these models and evaluate the effect of distributional assumptions on the target variable by comparing linear mixed models with Tweedie generalized linear mixed models. The results show that for their case-study, the Tweedie distribution is well suited to model and predict the loss cost on a contract. Additionally, incorporating contract-specific risk factors in the predictive model improves performance and allows for improved risk differentiation in their workers' compensation insurance portfolio. Overall, this paper provides valuable insights into how actuaries can effectively use predictive modeling techniques to assess loss costs on contracts while accounting for hierarchically structured risk factors. The findings have important implications for insurers looking to improve their pricing strategies and better manage risks associated with complex insurance products like workers' compensation.