Therefore, we propose the usage of sparse grid integration methods. The advantage of this approach is that the work which is necessary to solve the high-dimensional integration problems is nearly independent of the dimension, similar to Monte Carlo or Quasi-Monte Carlo methods. In the case of smooth integrands, however, which arise during the modelling of asset/liability management problems, the convergence rate of sparse grid methods is substantially higher than the rate of Monte Carlo-like methods. Further improvements bring the usage of nested quadrature formulas with maximum exactness, dimension-adaptive refinement and smoothness-preserving transformations.
These new numerical methods for the first time allow to efficiently solve the problems which are necessary for asset/liability management of insurance products. This way, it is possible to optimize such products with the help of numerical simulations and to estimate the arising risks under various model assuptions.