Oversikt av utländska aktuarietidskrifter

Abstract

Under Makehami's law, life annuities are expressed by incomplete gamma functions.     

On ratio estimates in simple random sampling with some practical applications

Abstract

The distribution of a ratio of two statistical variables has long been of gr,eat interest, especially with regard to the practical application within different branches. Several authors have also been interested in this subject, and a number of articles have been written on this problem on the basis of different assumptions. This problem seems now again to have been actualized by new experiences (ref. 2, 3,4) in the statistical sampling methods.     

Utility Functions

Abstract

This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. Then n companies (or economic agents) with random wealth are considered. They are interested in exchanging wealth to improve their expected utility. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. Two specific solutions are proposed. The first, believed to be new, is based on the synergy potential; this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. The second is the economic equilibrium originally proposed by Borch. As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained.     

Summary of Results of Survey of Seminar Attendees

Abstract

The Society of Actuaries undertook a three-phase research project on mortality improvement in the three NAFTA countries: Canada, Mexico, and the U.S. Phase 1 consisted of a literature review of papers on projecting mortality levels in the future and a study of the trend in mortality improvement during this century. Phase 2 consisted of a discussion of different facets of modeling mortality rates at a seminar attended by 79 experts (actuaries, demographers, economists, and medical researchers) representing different countries. The last session of the seminar consisted of the completion of a survey by the attendees to obtain input for Phase 3, which would analyze the impact of mortality improvement on the social security system of each country. This paper summarizes the results of the survey.

The survey results illustrate the difficulty in forecasting mortality levels, because the effects of many factors that could have significant impact on mortality rates are unknown. This suggests the need for dynamic forecasting, which allows for the possibility of random shocks. A majority of the survey respondents believe that stochastic forecasting models, despite their complexity, have significant potential to add value. Respondents also believe that both historical data and cause-specific mortality forecasts are useful as input and also in validating forecasts of the aggregate levels of mortality. The challenge is to develop more sophisticated forecasting models to produce results that are relatively easy to interpret and to communicate these results to the desired audiences, including the public and policymakers.

The survey results suggest that the aggregate effect of lifestyle changes, medical advances, diseases, catastrophe, and physical environmental changes is an increase in life span. However, there is much uncertainty about the future. Respondents expect that beyond the year 2020 the mean annual rate of reduction in mortality for males age 65 and over will average about 0.58% for Canada, 0.76% for Mexico, and 0.67% for the U.S. The results for the female age 65 and over population are 0.64%, 0.83%, and 0.70%, respectively. The age 65 and over population is expected to see larger percentage reductions in mortality than the 0–14 and 15–64 populations. The reductions in male and female mortality will be ultimately the same, and the mortality levels in the three countries will ultimately converge, although differences may persist for decades.     

A Regime-Switching Model of Long-Term Stock Returns

Abstract

In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskedastic model. The distribution function of the regime-switching model is derived. Prices of European options using the regime-switching model are derived and implied volatilities explored. Finally, an example of the application of the model to maturity guarantees under equity-linked insurance is presented. Equations for quantile and conditional tail expectation (Tail-VaR) risk measures are derived, and a numerical example compares the regime-switching lognormal model results with those using the more traditional lognormal stock return model.     

The Impact of the Inpatient Prospective Payment System and Diagnosis-Related Groups

Abstract

The outpatient prospective payment system for the Medicare program became effective Aug. 1, 2000, as mandated by the Balanced Budget Act of 1997. This outpatient program complements Medicare’s inpatient prospective payment system, which was introduced in 1983. A survey of the literature over the past 20 years is undertaken to review the effects of the inpatient prospective payment system and diagnosis-related groups (DRGs) on inpatient hospital utilization, expenditures, and outcomes. The level of the DRG payment has been questioned, as well as the process of adjusting the payment levels from one year to the next. In addition, past research has speculated that the DRG classification may not be sensitive to severity and is subject to coding ambiguities. These conclusions can be used as input to future research on the new outpatient program, as well as updating research on the inpatient program.     

Forward and spot exchange rates in a bivariate TAR framework

Structural exchange rate models explain only a small part of the movements in dollar exchange rate. Recent empirical work has focused on the failure to account for nonlinearities in the data generating mechanism, as an explanation of this bad performance. Here two bivariate threshold autoregressive models for the spot and forward exchange rates are considered. In the first model the regimes are determined by the log difference of the two rates; in the second one the regimes are driven by the forward spot no-arbitrage condition. These processes are able to capture the ‘swing’ behaviour observed in the exchange rate market. Finally the forecasting ability of the models for the dollar/DM exchange rate is evaluated by stochastic simulation.