Efficient Deterministic Numerical Simulation of Stochastic Asset-Liability Management Models in Life Insurance

New regulations, stronger competitions and more volatile capital markets have increased the demand for stochastic asset-liability management (ALM) models for insurance companies in recent years. The numerical simulation of such models is usually performed by Monte Carlo methods which suffer from a slow and erratic convergence, though. As alternatives to Monte Carlo simulation, we propose and investigate in this article the use of deterministic integration schemes, such as quasi-Monte Carlo and sparse grid quadrature methods. Numerical experiments with different ALM models for portfolios of participating life insurance products demonstrate that these deterministic methods often converge faster, less erratic and produce more accurate results than Monte Carlo simulation even for small sample sizes and complex models if the methods are combined with adaptivity and dimension reduction techniques. In addition, we show by an analysis of variance (ANOVA) that ALM problems are often of very low effective dimension which provides a theoretical explanation for the success of the deterministic quadrature methods.