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: 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 stochastic model in continuous time to characterize the ultimate benefit to be derived by a group of similar workers from their career membership in pension plans. This characterization is in terms of termination rates, vesting rules, plan types and periods of employment. The employment termination pattern is represented by a renewal process and a reward function is introduced to unify different plan types. A number of basic functions are then deduced to represent termination benefits, retirement benefits and the loss due to delayed vesting. An analysis of these functions lead to a number of conclusions regarding the comparative effects of delayed vesting in different plans. From Actuarial Research Clearing House 1981, Vol. 1.

Description: In this article, the authors introduce a new policy-making model for pension plan funding which openly represents the uncertainty. The word 'policy' is used here to indicate a strategy which is intended to be followed most [but not necessarily all] of the time. In unusual circumstances, the policy will have to be modified at the end of the year to retain qualification. However, the frequency with which this remedial action is needed is controllable by the actuary [unlike the method of using expected values]. The simple substitution of expected values of random quantities produces an unknown frequency of last minute remedial actions at possibly disastrous investment costs to the pension plan. However, with this paper's techniques, once the actuary acknowledges the uncertainty associated with the various aspects of the pension plan, he/she can explicitly trade off the costs associated with remedial actions, tax penalties, etc. with the investment returns in order to meet the pension plan goals. The method that this paper introduces is a new Chance-Constrained Programming approach to selecting annual contribution levels and asset allocation [holding other factors fixed] that the authors believe will better fit the employer's goals while recognizing the many risks and constraints associated with defined benefit plans. From Actuarial Research Clearing House 1993, Vol. 3.