A Neural Network approach to measure health insurance risk

This work presents a set of neural network applications to health insurance pricing. In recent years, the actuarial literature involving machine learning in insurance pricing has flourished. However, most actuarial machine learning research focuses on car and property and casualty insurance. While, the use of such techniques in health insurance is yet to be explored. In this manuscript, we discuss the use of neural networks to set the price of an health insurance coverage following the structure of a classical frequency-severity model. We consider neural networks to estimate claim frequency and severity. In particular, we introduce Negative Multinomial Neural Networks to jointly model the frequency of possibly correlated medical claims. We then complete the frequency-severity approach proposing Gamma Neural Networks to estimate the expected claim severity. We then go beyond the frequency-severity framework adopting a quantile approach that allows gauging the potential riskiness of a given policyholder. Namely, we discuss the estimation of conditional quantiles of aggregate claim amounts embedding the problem in a quantile regression framework using the Neural Network approach. As the first step, we consider Quantile Regression Neural Networks (QRNN) to compute quantiles for the insurance ratemaking framework. As the second step, we propose a new Quantile Regression Combined Actuarial Neural Network (Quantile-CANN) combining the traditional quantile regression approach with a Quantile Regression Neural Network. In both cases, we adopt a two-part model scheme where we fit a logistic regression to estimate the probability of positive claims and the QRNN model or the Quantile-CANN for the positive outcomes. Through a case study based on a health insurance dataset, we highlight the overall better performances of the different neural network models with respect to more established regression models (such as GLMs and quantile regression), both in terms of accuracy and risk diversification.