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

Anne-Sophie Krah,Zoran Nikolić,Ralf Korn

doi:10.3390/risks8010021

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 generalized linear model (GLM) and generalized additive model (GAM) methods to multivariate adaptive regression splines (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.

Highlights

The Solvency II directive of the European Parliament and European Council (2009) requires from insurance companies a derivation of the solvency capital requirement (SCR) using the full probability distributions of losses over a one-year period
The methods we present range from ordinary and generalized least-squares regression variants over generalized linear model (GLM) and generalized additive model (GAM) approaches to multivariate adaptive regression splines and kernel regression approaches
For example, function gam(·) in R package mgcv of Wood (2018) for a practical implementation of GAMs admitting these types of basis functions and using the PIRLS algorithm, which we present below

Summary

Introduction

The Solvency II directive of the European Parliament and European Council (2009) requires from insurance companies a derivation of the solvency capital requirement (SCR) using the full probability distributions of losses over a one-year period. Lacking an analytical valuation formula for the losses in a one-year period, life insurers with an internal model are supposed to utilize a Monte Carlo approach usually called nested simulations approach (Bauer et al (2012)). By applying suitable approximation techniques like the least-squares Monte Carlo (LSMC) approach of Bauer and Ha (2015), the insurers are able to overcome these computational hurdles though They can implement the LSMC framework formalized by Krah et al (2018) and applied by, for example, Bettels et al (2014), to derive their full loss distributions.

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Conclusion