A parametric model to price a portfolio of single-premium life insurance policies and to decompose its longevity risk

In this paper, the authors propose a statistical mathematical model to price an insurance portfolio consisting of single-premium life insurance policies, to calculate its variance and its longevity risk. The novelty introduced by the authors is that in their framework it is assumed that the outflows, namely the indemnities that are paid to the insured in life when the policies expire, are discounted at an uncertain interest rate. Other relevant hypotheses are that both the premium and the indemnity established by the insurance contract are constant until expiry and that the survival function of the policyholders is exponential. The authors show that both the price and the variance of the portfolio depend mainly on the speed at which the discount rate varies between the period of subscription of the policies and their expiry date, but also on the average value of this interest rate in the same period.