Long-Term Stability of a Life Insurer's Balance Sheet

Abstract

In this paper we devise a general, stochastic asset-liability management model for life insurance companies, based on the work of Gerstner et al. (2008). While the basic concept and structure are similar, we expand their model and specify several aspects in greater detail. One of the main extensions is the incorporation of new business, i.e. the addition of newly concluded contracts and thus insured in each period. This leads to new results on the consistency of the balance sheet equations. We can then utilize these to analyze the long-term behavior and the stability of the components of the balance sheet for different asset-liability approaches. Furthermore, we explicitly address the problem of the efficient simulation of a given large insurance portfolio by proposing an approach for the generation of cohorts and the integration of new contracts.