Multiple Life Insurance

Abstract

Consider m lives with initial ages x ₁, x ₂, ... , x _m . For simplicity we denote the future lifetime of the kth life, T(x _k )in the notation of Chapter 2, by T _k (k =1, ... , m). On the basis of these m elements we shall define a status u with a future lifetime T(u). We shall accordingly denote by _t p _u the conditional probability that the status u is still intact at time t, given that the status existed at time 0; the symbols q _u , μ _u+t etc., are defined in a similar way. We shall also consider annuities which are defined in terms of u. The symbol ä _u , for instance, denotes the net single premium of an annuity-due with 1 unit payable annually, as long as u remains intact. We shall also analyse insurances with a benefit payable at the failure of the status u. The symbol Ā _u would for instance denote the net single premium of an insured benefit of 1 unit, payable immediately upon the failure of u.