Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

TL;DR

This paper explores machine learning techniques to improve proxy modeling for life insurance companies under Solvency II, aiming to efficiently estimate loss distributions with limited simulations.

Contribution

It introduces and analyzes adaptive machine learning methods for proxy modeling, combining various regression techniques within the LSMC framework.

Findings

Machine learning methods can effectively replace traditional regression in LSMC.

The approaches demonstrate strong out-of-sample performance.

Theoretical justification supports combining different regression ingredients.

Abstract

Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the least-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over GLM and GAM methods to MARS and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.