Numerical Analysis

To illustrate results, this chapter introduces an academic as well as a very simplified insurance specific setup. The academic setup allows a derivation of an analytical solution for \(\mathbb {E}\left[ G(X) \right] \) in the moment- and \(q_\alpha ^X\) in the quantile-based case. Hence, such an example is especially relevant for our almost sure considerations because the illustration of a.s. rates requires at least an analytical solution. In the insurance specific part we introduce, first, an ALM model and describe its components. Second, we use this model to compare our confidence interval method to the already existing one of Lan et al. (2007b) in a practical setup. All simulation studies were performed on a standard laptop (processor: Intel core i7-1165G7, with 2.8 GHz, RAM: 16 GB) and all implementations were carried out in MATLAB 2018b.