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 is Mr. Gerber's proof of the Schuette-Nesbitt formula.

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.

Description: The purpose of this paper is to discuss computer application, the management of an insurance enterprise in an automobile insurance marketplace wherein a number of insurers compete for marketshare and profit. The paper begins with a description of the computer program next, a cursory description of the model is given then, the assumptions of the model are discussed next, potential future modifications are discussed and, finally, a prognosis is given.

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: This paper proposes to put the environment into financial markets. It explains how to do it, and why the financial approach is practically the only one able to stop and invert environmental degradation. The author concentrates on deforestation which is the largest environmental problem in the third world, and explains how to start the project and what kind of optimization problems should be solved for applications of the project.

Description: The purpose of this article is to provide an overview of soft computing applications in actuarial science. Soft computing refers to modes of computing in which precision is traded for tractability, robustness and ease of implementation.

Description: This paper presents a new methodology for obtaining fast algorithms and closed form solutions for pricing callable bonds in continuous time models. Results are directly applicable to regulatory scenario testing, immunization and market value accounting.

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: This is a letter to Professor Ralph Garfield in response to his contribution to the 1978.1 issue of ARCH. It answered his question concerning the non-applicability of an identity.