Description: The authors offer a method for estimating parameters for well-known three-parameter models of force of mortality. The method involves fitting a series of linear regressions, and finding the least-squares estimates of all the parameters by using the Golden Section Search method. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This paper discusses the numerical stability of Panjer's recursion in computing aggregate claims distributions. From Actuarial Research Clearing House 1993, VOL. 1.

Description: This paper provides a description of a method that one can use to develop an estimate of accident year incurred losses if the only available data is aggregate paid losses by calendar year for a number of calendar years. An exhibit demonstrating the use of this method follows this description. From Actuarial Research Clearing House 1993, VOL. 3.

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: This paper discusses the validity of model year rating for private passenger automobile coverages other than physical damage. While the techniques employed are elementary, the result is of interest to providers as well as purchasers of automobile insurance. From Actuarial Research Clearing House 1993, VOL. 3.

Description: The purpose of this paper is to present a parsimonious parametric model that explains the pattern of mortality for select and ultimate mortality tables. Specifically, the author modeled the combined rates found in the 1965-70 ALB Basic Tables. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper focuses on the fact that life and annuity reserves that are determined from discounted case flows mask the dynamic nature of interest rates. To study this effect in a stochastic interest environment, the authors look at a change in discounted reserves. By looking at the appropriate measure of change, the paper explores potential short-term consequences of changes in the interest environment.

Description: The main aim of this paper is to apply some of the techniques of modern time series and econometric analysis to analyse investment data in order to better understand the nature of long run relationships in investment series typically used in stochastic investment models. The paper attempts to identify and address fundamental issues that need to be considered before developing a particular stochastic investment model.

Description: This 1997 presentation from the 32nd Actuarial Research Conference develops a stochastic generator for the generation of scenarios of the S&P 500 index, dividend yield, consumer price index, and U.S. Treasury yields. The authors first create a set of 'stylized facts' for these series. They estimate statistical models for these series. These in-sample statistical models are themselves not suitable for generation of scenarios for decision making, but instead are additional 'stylized facts' that assist in model development. The 'best' statistical model according to standard statistical model selection criteria can easily lead to a model that is highly unsuitable for generation of scenarios for decision making. The authors develop a stochastic generator that is suitable for decision making under uncertainty.

Description: This paper presents an approach in which a defective renewal equation is solved in terms of a related compound geometric distribution. The advantage of this approach is discussed. The authors then apply this approach to a defective renewal equation which involves the time of ruin, the surplus before ruin and the total deficit at the time of ruin. They show how to compute the moments of the time of ruin as well as the joint distribution of the surplus before ruin and the deficit at the time of ruin. Two important cases in terms of claim size distributions are considered in detail. First, the authors consider exponential claim size distributions. They then consider a combination of two exponentials. The moments of the time of ruin are given in both cases.