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Markov chains play a key role in a vast number of areas, including life insurance mathematics. Standard actuarial quantities as the premium value can be interpreted as compressed, lossy information about the underlying Markov process. We introduce a method to reconstruct the underlying Markov chain given collective information of a portfolio of contracts. Our neural architecture explainably characterizes the process by explicitly providing one-step transition probabilities. Further, we provide an intrinsic, economic model validation to inspect the quality of the information decompression. Lastly, our methodology is successfully tested for a realistic data set of German term life insurance contracts.

Despite the high importance of grouping in practice, there exists little research on the respective topic. The present work presents a complete framework for grouping and a novel method to optimize model points. Model points are used to substitute clusters of contracts in an insurance portfolio and thus yield a smaller, computationally less burdensome portfolio. This grouped portfolio is controlled to have similar characteristics as the original portfolio. We provide numerical results for term life insurance and defined contribution plans, which indicate the superiority of our approach compared to K-means clustering, a common baseline algorithm for grouping. Lastly, we show that the presented concept can optimize a fixed number of model points for the entire portfolio simultaneously. This eliminates the need for any pre-clustering of the portfolio, e.g. by K-means clustering, and therefore presents our method as an entirely new and independent methodology.

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 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 might change over time.