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: This paper shows that the Esscher transform is an efficient technique for valuing derivative securities if the logarithms of the prices of the primitive securities are governed by certain stochastic processes with stationary and independent increments. From the Transactions of Society of Actuaries 1994, Vol. 46.

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: 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.

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: 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 shows that the Esscher transform is also an efficient technique for valuing derivative securities if the logarithms of the prices of the primitive securities are governed by certain stochastic processes with stationary and independent increments. Two applications are presented, the first for valuing a European call option and the second for pricing derivative securities of multiple risky assets.

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

Description: The purpose of this note is to show how certain formulas of life contingencies can be derived almost painlessly under the uniform distribution of deaths assumption.

Description: The presentation of the simplex algorithm in 'A Study Manual For Operations Research' [edited by Eugene A. Narragon] is difficult to follow. The purpose of this note is to show that a better understanding can be obtained by means of a geometric interpretation and the exchange method.