  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.
