Description: This paper is a theoretical examination of the structure of the property-casualty insurance industry using economic theory to compare companies with agency distribution versus direct distribution. The purpose of the paper is to justify the existence of both types of distribution systems in equilibrium.

Description: This paper studies the internal rate of return of a finite series of cash flows in terms of three natural axioms. Examples of rate of return functions are constructed and their economic significance is discussed. From the Actuarial Research Clearing House 1992 Vol. 1.

Description: The two-parameter Pareto distribution is a commonly used model in reliability and risk modeling. Minimum variance unbiased estimates of the parameters of Pareto distribution are not known. In this paper, we propose and investigate a method of estimation of the parameters of the Pareto distribution. This method is based on minimization of the Kolmogorov-Smirnov distance between the empirical cumulative distribution function [cdf] and the cdf of the Pareto distribution.

Description: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

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: Most computations that are done within actuarial science entail using discrete death rates associated with incremental ages. It's not that continuous death rates cannot be used, it's just that discrete values tend to be more convenient to work with. Of the various continuous probability distributions, the one most closely associated with actuarial science may be the Gompertz distribution. This paper takes a closer look at the Gompertz, starting with the motivation behind Benjamin Gompertz proposing this particular distribution. Then the paper develops procedures to estimate the parameters for this distribution, and it ends with a brief example of the procedures presented in the paper.

Description: This is a letter to readers of The Actuary from Arnold Dicke and Walter Lowrie to solicit opinions on the problem which seems to crop up each time an examination is to be set.

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 discusses some powerful uses of recursive functions, including: 1. Universal life, both for the calculation of target premiums and reserves. 2. Paid-up Rider. Recursive functions can directly determine a premium that precisely matures the rider. 3. Traditional Whole Life. Reserves can be efficiently calculated when needed instead of referring to a table of stored factors. From Actuarial Research Clearing House 1993, VOL. 3.

Description: The study is based on a sample of actuarial reports attached to the form 550C3, Schedule B, which were sent to the Department of Labor during the period June 1976 to May 1977.