Actuarial Pricing for Minimum Death Guarantees in Unit-Linked Life Insurance: A Multi-Period Capital Allocation Problem

We analyze an actuarial approach for the pricing and reserving of minimum death guarantees in unit-linked life insurance. After summarizing some results on mono-period risk measurement, we explain two possible strategies to deal with multi-period capital allocation problems. The first one uses no future information whereas the second one does. We explain how a cash-flow model can be used to perform the actuarial pricing and how we model the guarantee we are investigating. Next, we describe a simulation strategy which can be used to derive approximate distribution functions for the future reserves, capitals and total solvency levels in the approach where future information is used. From this strategy, average future capitals, which are needed in the cash-flow model, can be calculated. We test the simulation strategy and we compare both multi-period approaches.