Description: This paper presents a generalized profits released model which resolves the difficulties of the traditional analysis posed by products that have fluctuating profits and losses over time or have no initial investment. Discussions of the paper are included.

Description: In calculations involving the distribution of total claims in a risk theory setting, several authors have found it desirable to approximate a risk-theoretic distribution by use of the incomplete gamma function. A recent paper evaluated an excess loss ratio premium by use of a gamma distribution whose first and second moments agreed with those of the risk-theoretic loss distribution. A discussion of that paper pointed out that a translated gamma distribution allowed one to make the approximate distribution agree with the risk-theoretic distribution as far as the first three moments are concerned. The method presented in this paper allows one to make as many moments of the approximate distribution as desired agree with those of the risk-theoretic loss distribution. From Transactions of Society of Actuaries 1966, Vol. 18, Pt. 1, No. 52.

Description: This paper presents the general notion of a periodogram, following Elphinstone's approach. The paper then goes on to examine symmetric linear operators and their periodograms in preparation for the end discussion of periodograms of graduators.

Description: The purpose of this paper is to set forth a precise method of testing reserves based upon the time-honored accumulation formula, which requires the production of reserves and transactions by attained age.

Description: The purpose of this paper is to provide an introduction to mathematical principles applicable to pension funding under dynamic conditions of population growth, inflation, and automatic adjustment of benefits. From Transactions of Society of Actuaries 1976, Vol. 28.

Description: The basic principle introduced in this paper is that the expected value of receipts on any insurance policy is equal to the expected value of payouts. Using an expected value approach, rather than present values, offers an interesting conceptual framework which might provide a possible starting point in risk theory to consider statistical variation about these expected values.

Description: The primary purpose of this paper is to set forth one method of evaluating vested pension costs and to suggest a simple way for the actuary to make provision in his pension cost calculations for specific vesting schedules. From Transactions of Society of Actuaries 1966, Vol. 18, Pt. 1, No. 52.

Description: In March this year a charter for the new corporation, the College Retirement Equities Fund, was granted by the State of New York and it is expected that within a few months the Fund will begin operations as a supplement to TIAA annuities. The purpose of this paper is to describe this rather novel type of corporation, which presents some unusual and interesting actuarial problems. Comparisons of the performance of fixed annuities vs. variable annuities are provided.

Description: This paper sets out, in algorithm form, a one-factor term structure model of interest rates and illustrates the application of such a model to the valuation of loans with prepayment provisions. From the Transactions of Society of Actuaries 1994, Vol. 46.

Description: Provides a methodology for determining the value of the share of a particular individual in a joint and survivor annuity held by a trust.