Description: These notes are a follow-up to the paper 'Introduction to the Dynamics of Pension Funding' by the same authors and published in Transactions of Society of Actuaries 1976, Vol. 28. The purpose of that paper was to provide an introduction to mathematical principles applicable to pension funding under dynamic conditions of population growth, inflation, and automatic adjustment of benefits. The first note discusses a general contribution formula and a number of special cases and modifications. The second note concerns aggregate cost funding when the actuary uses assumptions about cost factors which differ consistently from cost experience. The final note concerns the variation of the annuity unit under a variable annuity program patterned after the plan employed by the College Retirement Equities Fund [CREF]. From Actuarial Research Clearing House 1981, Vol. 1.

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: Traditional pension mathematics assumes that mortality rates are fixed at a valuation date. If mortality rates reduce after a valuation date, the liabilities of a defined benefit plans 'DB plans' increase, leading to deficits. Such deficits are somewhat unpredictable, because the evolution of mortality rates is a random process. This problem, which is often called longevity risk, makes the maintenance of DB plans difficult. The International Accounting Standards Board 'IASB' has plans to tackle the arduous problem of how to disclose longevity risk on financial statements. The IASB was established in 2001 to create universal accounting standards, called International Accounting Reporting Standards 'IFRSs'. A primary objective of this paper is to propose a number of methods that can help actuaries and plan sponsors quantify and disclose longevity risk.

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 subject of this paper is a financial model for pension planning purposes. The focus of the model is from an individual's point of view with the idea to assist him/her in planning for a financially secure retirement income. The model is dynamic and stochastic, operates in nominal and real terms, and goes beyond the age of retirement. From Actuarial Research Clearing House 1981, Vol. 1.

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 "Think Tank on Steroids" group at the DI and LTC Insurers’ Forum brainstormed about what the United States should do in order to deal with the impending Long-Term Care problem in the United States. The group’s ideal plan for dealing with Long Term Care can be thought of as a three-legged stool. The legs are private savings and assets (including tax-advantaged LTC savings accounts), Long-Term Care Insurance (including smaller, more affordable products), and support from the family. The Medicaid system ought to be reformed so that it is only available to people who have exhausted all other options. The ongoing Think Tank will continue this conversation and publish a white paper detailing the Think Tank’s solution to the problem.

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.