Modeling Churns: A Pricing Perspective

Churn models model whether or not an insured will deliberately leave a portfolio or remain, which is a standard classification problem. These models are very popular in marketing and client management; machine learning techniques and other advanced statistical methods are widely used and researched within this application. However, they seem to be neglected by the actuarial community.

I believe that churn models are also of great use in an actuarial context, namely in Pricing. This is, because often actuarial premiums contain implicit assumptions on the risk structure of the portfolio. This is the case whenever the premiums are not incorporating all relevant risk factors. Hence, changes in the underlying portfolio structure can lead to deviations of the correct actuarial premium. In other words: Deviations from the expected claims are not only due to the randomness of claims, but also due to the changes in portfolio structure. Churn decisions are a priori not random, and premium (changes) are main drivers. This leads to the second purpose of a churn model in pricing: it helps to set the adequate market premium, as this also impacts the portfolio.

The proposed talk will be based on my Master Thesis at ETH Zurich and hopefully other research undertaken since then. It investigates the use of churn models in an actuarial pricing context of a mandatory swiss health insurer. In this setting, we have a unitary premium for adults. Also, the scope of cover is the same for all competitors, which allows a direct comparison of premiums of the competitors. We fit several logistic regression, classification tree and gradient boosting machine models to a very large data set. We reflect the particular requirements of actuarial pricing by introducing a pricing loss function that measures the impact of the churn prediction error on the predicted profits. This is a new approach to measure model performance and could be an alternative to using standard metrics like AUC. We also incorporate the premiums of the top 5 competitors as explanatory variables, allowing to model the impact of premium difference on the churn rate and calculating premium sensitivities.