Description: In this paper, the coefficients of the minimum-Rz moving-weighted-average formulas are derived using matrix algebra and the method of Lagrange multipliers. Reviewer's note: This mathematics can be useful in the graduation process of mortality and morbidity table construction

Description: This paper considers the distribution of aggregate claims of an insurer. The general form of the distribution is considered initially, and, after a few mild restrictions are imposed, it is characterized as being a compound distribution. Followed by one submitted discussion paper.

Description: A study note for Exam MFE (Actuarial Models–Financial Economics Segment). This document describes the parameter d (delta) in the Black-Scholes formula.

Description: The following problem is from the 1968 Society of Actuaries Part 4 Examination on Life Contingencies. It is an instructive problem because it interweaves joint-life functions with single-life reserves.

Description: This paper discusses the time value of ruin in a Sparre Anderson Model and presents multiple equations, including Lundberg's fundamental equation.

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: Actuaries measure, model, and manage risks. Risk associated with the investment function is a major uncertainty faced by many insurance companies. Actuaries should have knowledge of the asset side of the balance sheet of an insurance company and how it relates to the liability side. From Securitization of Insurance Risk: The 1995 Bowles Symposium, M-FI97-1.

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: A short note on derivatives of decreasing life annuities that was motivated by Exercise 5.35 on page 156 of 'Actuarial Mathematics'. Actuarial Research Clearing House 1993 VOL. 2

Description: The Cauchy integral formula is applied to derive various results on divided differences.