# 14-117/IV/DSF80 (2014-08-29)

Author(s)
Marcus C. Christiansen, University of Ulm, Germany; Michel M. Denuit, Université Catholique de Louvain, Belgium; Jan Dhaene, Katholieke Universiteit Leuven, Belgium, University of the Free State, South Africa
Keywords:
life insurance, multistate models, Markov process, surrender value, Cantelli theorem
JEL codes:
G00

Premiums and benefits associated with traditional life insurance contracts are usually specified as fixed amounts in policy conditions. However, reserve-dependent surrender values and reserve-dependent expenses are common in insurance practice. The famous Cantelli theorem in life insurance ensures that under appropriate assumptions surrendering can be ignored in reserve calculations provided the surrender payment equals the accumulated reserve. In this paper, more complex reserve-dependent payment patterns are considered, in line with insurance practice. Explicit formulas are derived for the corresponding reserve.