A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies

Abstract

The Solvency II directive asks insurance companies to derive their solvency capital requirement from the full loss distribution over the coming year. While this is in general computationally infeasible in the life insurance business, an application of the Least-Squares Monte Carlo (LSMC) method offers a possibility to overcome this computational challenge. We outline in detail the challenges a life insurer faces, the theoretical basis of the LSMC method and the necessary steps on the way to a reliable proxy modeling in the life insurance business. Further, we illustrate the advantages of the LSMC approach via presenting (slightly disguised) real-world applications.

An aspect of optimal regression design for LSMC

“…1 Convergence under less restrictive assumptions than those from [New97] was proved in [Ben17]. It is stated in [KNK18] that convergence also holds in the slightly different setting closer to the actual implementations on the market in contrast to [BH15] which we are going to present here.…”

“…In recent years LSMC has gained a lot of attention also in the insurance business, where approximation algorithms are needed to calculate the capital requirements under the Solvency II regime, see e.g. [BBR10], [LHKB13], [BFW14], [KNK18]. The reason for the necessity of approximation is that a full nested stochastic calculation of the capital requirement would cause run times which as of today by far exceed the computing capacities of insurance companies.…”

“…Finally, the quality of the approximation is assessed using an out-of-sample validation. For more details on the LSMC algorithm we refer the reader to [BFW14] and [KNK18].…”

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

“…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. For example, 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. The central idea of this framework is to carry out a comparably small number of wisely chosen nested Monte Carlo simulations and to feed the simulation results into a supervised machine learning algorithm that translates the results into a proxy function of the insurer's loss (output) with respect to the underlying risk factors (input).…”

“…Our starting point is the LSMC framework from Krah et al (2018). In the following the same approach for the proxy derivation is assumed, we will only amend the calibration and validation steps.…”