A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension

A sensitivity analysis concept is introduced for prospective reserves of individual life insurance contracts as deterministic mappings of the actuarial assumptions interest rate, mortality probability, disability probability, etc. Upon modeling these assumptions as functions on a real time line, the prospective reserve is here a mapping with infinite dimensional domain. Inspired by the common idea of interpreting partial derivatives of first order as local sensitivities, a generalized gradient vector approach is introduced in order to allow for a sensitivity analysis of the prospective reserves as functionals on a function space. The capability of the concept is demonstrated with an example.