A Neural Network Approach for Pricing Correlated Health Risks

In recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on property and casualty insurance, while using such techniques in health insurance is yet to be explored. In this paper, we discuss the use of neural networks to set the price of health insurance coverage following the structure of a classical frequency-severity model. In particular, we propose negative multinomial neural networks to jointly model the frequency of possibly correlated medical claims and Gamma neural networks to estimate the expected claim severity. Using a case study based on real-world health insurance data, we highlight the overall better performance of the neural network models with respect to more established regression models, both in terms of accuracy (frequency models achieve an average out-of-sample deviance of 8.54 compared to 8.61 for classical regressions) and risk diversification, as indicated by the ABC lift metric, which is (Formula presented.) for neural networks versus (Formula presented.) for traditional models.