Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance

TL;DR

This paper introduces a neural method to reconstruct and validate the underlying Markov chain in life insurance, enabling better understanding of the process from compressed portfolio data.

Contribution

It presents an explainable neural architecture for Markov chain reconstruction and an economic validation approach, applied successfully to real insurance data.

Findings

Effective reconstruction of Markov chains from portfolio data

Explainable transition probability estimation

Validated on real German life insurance data

Abstract

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.