Description: The paper gives two criteria for fit and uses two different criteria to transform an initial graduation into one with better fit. It is shown that the two sets of criteria give the same transformation. The mathematical relationships between the two sets of criteria are then derived. It is clear from those relationships that when one set of criteria is small, the other set is small [but reasonably the same]. Some general comments on various measures of fit are made.

Description: This paper provides provide mathematically-founded insights for how climate change and water access will impact Californian agriculture in the coming decades.

Description: This paper presents a proof using the general mean value theorem that under specified conditions, the insurance premium for complete protection against a specified loss will decrease with increasing wealth. From Actuarial Research Clearing House 1994, Vol. 1.

Description: In the present paper, we propose and investigate a numerical method of computing the probability distribution of S. Inversion of the Laplace transform moment generating function is shown to be a better approach than the existing recursive method for find the distribution of sum of several independent random variables. In the continuous case, in many situations, numerical inversion needs to be used to compute the probability distribution function of the sum.

Description: This article investigates the simplicity of the Balducci hypothesis, and compares the fractional-age death probability given by three widely used assumptions: uniform distribution of deaths, the Balducci hypothesis, and constant force of mortality [1, 2].

Description: It is assumed that the force of interest varies as an auto-regressive process of order 2, AR[2]. The moments of the accumulated value of 1 paid at the beginning of each period, for n periods, are developed using moment generating functions.

Description: This paper is the final report in a project commissioned by the Society of Actuaries Social Security Committee. The paper considers a variety of possible risk classification factors that could be used in estimating the value of any mortality based benefit for retirees. As many countries consider mandatory individual retirement accounts as their answer to a secure Social Security system, the question arises as to whether all workers can get true 'market value' annuities when they retire. It is clear today that private sector life annuities are priced assuming that the applicant is healthy-very healthy. Very little underwriting or risk classification now exists in the individual annuity marketplace. This paper reviews 45 recent research papers that look at factors that affect mortality after retirement. In particular, factors that seem to be important in predicting retirement mortality include: age, gender, race and ethnicity, education, income, occupation, marital status, religion, health behaviors, smoking, alcohol, and obesity. For each factor, this paper gives highlights relative to the named factor of the impact expected from that variable as described in the 45 reviewed research papers.

Description: This article presents the needed mathematical techniques and obtains values for active life expectancies in which dependent lives are followed after regaining independence. Secondly, projections of active life expectancies are developed to the year 2080, under three sets of assumptions, for 65 year old men and women. Finally, estimates of the average numbers of years of dependency in ADL prior to death of 65 year old men and women are provided under alternate sets of assumptions. From the Actuarial Research Clearing House 1991 VOL. 2.

Description: This paper develops a theory for the valuation of some kinds of interest sensitive cash flows. A process is derived which takes as input, assumptions about the capital markets and policy holder behaviour, and produces as output interest and decrement assumptions which can be used for conventional actuarial discounting. The methodology is illustrated using some idealized, but tractable, models of conventional non-par whole life insurance. The method is also applied to a simple Universal Life plan. The paper concludes by considering some of the problems encountered when applying the ideas to more practical problems.