Multiple Life Insurance

Consider> m lives with initial ages xi, x 2 x m . For simplicity we denote the future lifetime of the fcth 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 would for instance denote the net single premium of an insured benefit of 1 unit, payable immediately upon the failure of u.