Mean-field Libor market model and valuation of long term guarantees

Abstract: Existence and uniqueness of solutions to the multi-dimensional mean-field Libor market model (introduced by [7]) is shown. This is used as the basis for a numerical asset-liability management (ALM) model capable of calculating future discretionary benefits in accordance with Solvency~II regulation. This ALM model is complimented with aggregated life insurance data to perform a realistic numerical study. This yields numerical evidence for heuristic assumptions which allow to derive estimators of lower and upper bounds for future discretionary benefits. These estimators are applied to publicly available life insurance data.