Description: In this paper two theorems concerning the optimality of the perfect-fit and perfect-smoothness graduations are proved. Two examples are presented and some difficulties with regard to computational feasibility are reviewed. A discussion of the paper follows. From Transactions of Society of Actuaries 1978, Vol. 30.

Description: Gross premium calculation methods may be arbitrarily separated into: a- Type 1 methods those which initially have commissions and other per cent of premium expenses in the denominator and b- Type 2 methods those which initially have commissions and other per cent of premium expenses in the numerator. The traditional Type 1 methods directly calculate the gross premium. The purpose of this paper is: 1. to present a Type 1 method of gross premium calculation which does the following: a Incorporates the cost of reinsurance into the gross premium calculation and may be shown as a level annual cost over the gross premium calculation period. b Calculates the effect on profit margins of a change in the retention limit without redoing the original calculation. c Calculates the premiums needed to break even e.g., amortize the initial investment in surplus at the end of each policy year as a by-product. d Calculates the profit or loss generated in each policy year or over any number of policy years for any gross premium without redoing the original calculation or first using a trial gross premium. e Directly solves for the gross premium that will produce any specified profit over any number of policy years without redoing the original calculation or first using a trial gross premium. f Directly solves for the premium that will produce a specified yield on surplus invested in new business by a flexible technique not first involving the use of the renewal net premium or any other preliminary gross premium. 2. to provide a mathematical definition of a financially meaningful average policy size which recognizes the cost of reinsurance. 3. to provide for mathematical definitions of common measures of profit, and the mathematical relationships between them. 4. To establish formulas expressing the effect of changes in various assumptions used in the gross premium calculation as a lev

Description: The primary objective of the paper was to develop a straightforward method for constructing an interpolation formula of finite range with desired properties stipulated in advance. This paper had in view mainly the application to polynomial interpolation as used in actuarial work. Followed by 2 discussion papers submitted