Description: The author comments on the article Exposure Formulas Based on the Assumption of Uniform Distribution of Deaths written by T.N.E. Greville.

Description: In this paper the authors analyze data from group medical expense insurance claims and show that many insurance loss distributions have very 'heavy tails' because large losses represent a disproportionate fraction of the total cost. They also present a simple model to reproduce and explain the large loss behavior. From Actuarial Research Clearing House 1990, VOL. 2

Description: In estimating mortality rates from the experience of a life insurance company or employee-benefit plan, it is expedient, because of the movement into and out of the covered group on dates other than birthdays or policy anniversaries, to make some assumption about mortality over a fractional part of a year of age. This paper describes and develops the concept of 'exposure' with regard to the more commonly known methods of estimating the rate of mortality, and proposes a fourth methodology. From the Actuarial Research Clearing House 1978, Vol.2.

Description: In this paper, given the three moments of the claim amount, the authors find the di-atomic and the di-exponential distributions that fit the given three moments. They use ruin probability formulas when the claim amount is discete or is a combination of exponentials to compute ruin probabilities based on the claim amount distribution which match the first three moments of the original claim amount distribution. Actuarial Research Clearing House 1992 VOL. 1

Description: Australia has conducted ten national censuses since World War II: in 1947, 1954, 1961 and at five-year intervals through 1996. Life tables have been prepared in connection with each of these censuses except the most recent one, for which data is still being collected.

Description: Multiple decrement theory traditionally is based on the assumption that competing causes of decrement are stochastically independent even though this assumption is usually not true in reality. This paper presents some fundamental results towards a dependent decrement theory. First, the author shows how to model dependence with copula functions, then he presents a theorem that characterizes the mathematical relationship between the crude and net probabilities when the decrements are dependent, and finally he applies the results by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This article provides an an alternate, statistical approach, to graduation. Both single and multiple decrement models are considered and theoretical results are obtained for some specific mortality models. From: ACTUARIAL RESEARCH CLEARING HOUSE, 1979 VOL. 2.

Description: Equity-indexed annuities [EIA's] are the fastest growing annuity products. An appealing feature of an EIA to its holder is that it contains path-dependent options which allow the policyholder to participate in favorable investment performance while maintaining a minimum guarantee on the benefit level. Studying the valuation problem of path-dependent options enables us to provide needed information to insurance companies on the costs of these options as well as investment strategy for their portfolios. The martingale approach by Gerber and Shiu [1994, 1996] enables us to solve some valuation problems in option pricing without knowing deep results in stochastic calculus such as the Reflection Principle and Girsanov Theorem. What is needed is the Laplace transform of certain distributions known by actuaries. This paper shows how to use Gerber and Shiu's approach to compute two defective density functions related to double barrier hitting probabilities of a geometric Brownian motion. The approach used here is simple and straightforward, and purely analytical. The authors then apply the formulas to value some exotic options whose payoffs are contingent on barrier hitting time.

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 that Balucci hypothesis imposed on a survivorship function over a closed interval is dual to the uniform distribution of deaths hypothesis imposed on the survivorship function over the same interval.