Description: In problem 24, Chapter 5, of Kellison's 'Fundamentals of Numerical Analysis' it is indicated how a divided difference can be expressed as a ratio of two determinants. This study note shows that this method works well also in the case where some of the arguments of collocation coincide. The rule is: If an argument occurs k times, the derivatives of the corresponding row up to order k-1 should be used in numerator and denominator.

Description: A presentation of a mathematics/statistics based approach for determining credibility factors for possible use in group health insurance premium rate setting and experience refund setting. Includes supporting mathematical proofs of approach. Followed by discussions submitted by several people

Description: This people provides a derivation of continuous and curtate inequalities of life contingent functions and shows how the proofs of the continuous inequalities are of an entirely different nature from the usual proofs for the curtate inequalities Followed by discussion papers submitted by several authors

Description: This paper presents a statistical and mathematical method to calculate Stop-Loss Premiums. It also includes a discussion of the paper. From Transactions of Society of Actuaries 1976, Vol. 28.

Description: This presentation shows that, if the options or guarantees are exercisable only at the moment of death of the policyholder, the mathematics simplifies to an elementary calculus exercise.

Description: This paper explores the principles upon which experience-rated group insurance currently is based and discusses the question of whether or not these principles are sound. Followed by discussion papers submitted by several authors

Description: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The classical model is generalized by discounting with respect to the time of ruin. The authors show how to calculate an expected discounted penalty, which is due at ruin, and may depend on the deficit at ruin and the surplus immediately before ruin.

Description: In classical collective risk theory, the aggregate claims process is assumed to be compound Poisson. In this paper the authors examine a more general model for the aggregate claims process: processes with independent, stationary and non-negative increments. From Actuarial Research Clearing House 1991, VOL. 1.

Description: In an increasing population the number of persons falls off from age to age more rapidly than does the stationary population of the life table. This can introduce a systematic bias into life table calculations. The first part of the paper describes an iterative procedure to correct for the bias, extends the method to multiple decrement and associated single decrement life tables, and demonstrates the magnitude of the bias involved. The second part of the paper summarizes the results of applying iterative life table techniques to 165 populations which encompass over a century's experience and include countries from all parts of the world. Followed by discussions submitted by several people

Description: This paper shows how some moment inequalities of probability theory can be applied in three different areas of actuarial science - compound interest, life contingencies and risk theory. From Transactions of Society of Actuaries 1986, Vol. 38.