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

Under the Solvency II regime, life insurance companies are asked to derive their solvencycapital requirements from the full loss distributions over the coming year. Since the industryis currently far from being endowed with sufficient computational capacities to fully simulatethese distributions, the insurers have to rely on suitable approximation techniques such as theleast-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wiselyselected simulations and to process their output further to obtain a risk-dependent proxy functionof the loss. In this paper, we present and analyze various adaptive machine learning approachesthat can take over the proxy modeling task. The studied approaches range from ordinary andgeneralized least-squares regression variants over generalized linear model (GLM) and generalizedadditive model (GAM) methods to multivariate adaptive regression splines (MARS) and kernelregression routines. We justify the combinability of their regression ingredients in a theoreticaldiscourse. Further, we illustrate the approaches in slightly disguised real-world experiments andperform comprehensive out-of-sample tests.