Modeling surrender risk in life insurance: theoretical and experimental insight

TL;DR

This paper investigates modeling surrender risk in life insurance, comparing various machine learning approaches, highlighting shortcomings of traditional assessments, and proposing probabilistic evaluation methods for better risk prediction.

Contribution

It introduces a comprehensive experimental analysis of modeling approaches and proposes time-dependent confidence bands for surrender rate predictions, addressing limitations of existing evaluation methods.

Findings

Resampling improves label prediction but biases probability estimates.

Models trained on resampled data predict significantly biased surrender probabilities.

Time-dependent confidence bands enhance practical assessment of surrender rates.

Abstract

Surrender poses one of the major risks to life insurance and a sound modeling of its true probability has direct implication on the risk capital demanded by the Solvency II directive. We add to the existing literature by performing extensive experiments that present highly practical results for various modeling approaches, including XGBoost, random forest, GLM and neural networks. Further, we detect shortcomings of prevalent model assessments, which are in essence based on a confusion matrix. Our results indicate that accurate label predictions and a sound modeling of the true probability can be opposing objectives. We illustrate this with the example of resampling. While resampling is capable of improving label prediction in rare event settings, such as surrender, and thus is commonly applied, we show theoretically and numerically that models trained on resampled data predict significantly biased event probabilities. Following a probabilistic perspective on surrender, we further propose time-dependent confidence bands on predicted mean surrender rates as a complementary assessment and demonstrate its benefit. This evaluation takes a very practical, going concern perspective, which respects that the composition of a portfolio, as well as the nature of underlying risk drivers might change over time.