Abstracts of Prize Winning Papers

"Stochastic life contingencies with solvency considerations" Transactions of the Society of Actuaries, Vol. 42, pp. 91-148. (Frees) (Awarded Halmstad Prize and Annual Prize)

The extension of the theory of life contingencies to a stochastic interest environment and its application to solvency valuation are discussed. Although life contingencies are widely used in traditional actuarial valuations of life insurance contracts, certain complications arise in a stochastic interest environment that are not evident when using traditional deterministic interest assumptions. In particular, many insurance functions can no longer be expressed in a simple form, resulting in a loss of the intuitive appeal of these functions. In this paper, a stochastic interest environment is introduced and analyzed in terms of its effects on insurance functions. Although the model is less general than others introduced in the literature, it is sufficiently flexible to handle the volatility and certain autocorrelation aspects of interest series. Its main advantage is the simple form of the resulting insurance functions and, hence, its intuitive appeal.

To examine the performance of a block of business, the assets as well as the liabilities are considered. For liabilities of a block of business under a common stochastic interest environment, limit theorems for approximating the behavior of sums of policies are no longer readily available. Even if the mortality experiences of the policies are independent, the liabilities are not independent because of the common interest environment. By considering assets as well as liabilities, matching of cash flows reduces the volatility of surplus, defined to be assets in excess of liabilities. In fact, under an extreme type of matching, limit laws for sums of homogeneous policies can be described under more general interest environments than those described above.

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"Annuity valuation with dependent mortality" Journal of Risk and Insurance 63, 229-261. (Frees, Carriere and Valdez) (Valdez was a doctoral student at the time the work was done). (Awarded Halmstad Prize and shared the Ed Lew Award)

Annuities are contractual guarantees, issued by insurance companies, pension plans, and government retirement systems, that offer promises to provide periodic income over the lifetime of individuals. It is well-known how to use univariate models of survivorship for valuing annuities. However, standard industry practice assumes independence of lives when valuing annuities where the promise is based on more than one life.

This paper investigates the use of models of dependent mortality for determining annuity values. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company to illustrate our methods, we calculate maximum likelihood estimates to calibrate the model. The estimation results show strong positive dependence between joint lives. This statistically significant result translates into real economic significance. That is, there is an approximate five percent reduction in annuity values when dependent mortality models are used compared to the standard models that assume independence. We show that the results are robust in terms of the choice of parametric family of distribution functions.

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"Forecasting Social Security actuarial assumptions" North American Actuarial Journal volume 1, No. 4, 49-82. (Frees, Kung, Rosenberg, Young and Lai) (Kung and Lai were UW doctoral students at the time the work was done). (Awarded Halmstad Prize and shared the Ed Lew Award)

This paper presents a forecasting model of economic assumptions that are inputs to projections of the Social Security system. Social Security projections are made to help policy-makers understand the financial stability of the system. Because system income and expenditures are subject to changes in law, they are controllable and not readily amenable to forecasting techniques. Hence, we focus directly on the four major economic assumptions to the system: inflation rate, investment returns, wage rate, and unemployment rate. Population models, the other major input to Social Security projections, require special demographic techniques and are not addressed here. Our approach to developing a forecasting model emphasizes exploring characteristics of the data. That is, we use graphical techniques and diagnostic statistics to display patterns that are evident in the data. These patterns include (1) serial correlation, (2) conditional heteroscedasticity, (3) contemporaneous correlations, and (4) cross-correlations among the four economic series. To represent patterns in the four series, we use multivariate autoregressive, moving average (ARMA) models with generalized autoregressive, conditionally heteroscedastic (GARCH) errors.

The outputs of the fitted models are the forecasts. Because the forecasts can be used for nonlinear functions such as discounting present values of future obligations, we present a computer-intensive method for computing forecast distributions. The computer-intensive approach also allows us to compare alternative models via out-of-sample validation and to compute exact multivariate forecast intervals, in lieu of approximate simultaneous univariate forecast intervals. We show how to use the forecasts of economic assumptions to forecast a simplified version of a fund used to protect the Social Security system from adverse deviations. We recommend the use of the multivariate model because it establishes important lead and lag relationships among the series, accounts for information in the contemporaneous correlations, and provides useful forecasts of a fund that is analogous to the one used by the Social Security system.

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"Understanding Relationships Using Copulas" (Frees and Valdez) North American Actuarial Journal volume 2, No. 1, 1-25. (Shared the Ed Lew Award)

This article introduces actuaries to the concept of ''copulas,'' a tool for understanding relationships among multivariate outcomes. A copula is a function that links univariate marginals to their full multivariate distribution. Copulas were introduced in 1959 in the context of probabilistic metric spaces. The literature on the statistical properties and applications of copulas has been developing rapidly in recent years. This article explores some of these practical applications, including estimation of joint life mortality and multidecrement models. In addition, we describe basic properties of copulas, their relationships to measures of dependence, and several families of copulas that have appeared in the literature. An annotated bibliography provides a resource for researchers and practitioners who wish to continue their study of copulas. For those who wish to use copulas for statistical inference, we illustrate statistical inference procedures by using insurance company data on losses and expenses. For these data, we (1) show how to fit copulas and (2) describe their usefulness by pricing a reinsurance contract and estimating expenses for pre-specified losses.

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"A Longitudinal Data Analysis Interpretation of Credibility Models" (Frees, Young and Luo) Insurance: Mathematics and Economics 24, 229-248.

In this paper, we develop links between credibility theory in actuarial science and longitudinal data models in statistics. Our primary contribution to actuarial science is to demonstrate that many additive credibility models can be expressed as special cases of the longitudinal data model. We, thereby, unify the many existing credibility models with this framework. In addition, a longitudinal data interpretation suggests additional models and techniques that actuaries can use in credibility ratemaking. We also apply standard statistical software, which has been developed to analyze longitudinal data models, to the private passenger automobile data of Hachemeister (1975).

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"International property-liability insurance consumption" Journal of Risk and Insurance 67, 73-90. (Browne, Chung and Frees). (Chung was a doctoral student at the time the work was done). (Awarded a Research award from the International Insurance Society)

During the 1980s and early 1990s, the world insurance market grew substantially.  In 1993 world insurance premiums were approximately $1.8 trillion, accounting for about 8 percent of world Gross Domestic Product compared to 4 percent in 1984.This study explains a substantial proportion of the variation in property-liability insurance consumption across OECD member countries. The study focuses on two lines of insurance - motor vehicle and general liability.  Our analysis indicates that economic conditions affect the demand for insurance differently across lines of coverage.  In particular, our results suggest income has a far greater effect on automobile insurance consumption than on general liability insurance consumption. 

Prior studies of property-liability insurance consumption were based on data that was aggregated across all non-life insurance lines. The current study indicates that additional insights can be gained by using disaggregated data when explaining variations in the international consumption of insurance.  The analysis reveals that the purchase of different lines of insurance is influenced differently by various economic and demographic conditions.  In particular we find that the percent of a country's insurance market controlled by foreign firms is negatively correlated with the purchase of motor vehicle insurance but positively correlated with the purchase of general liability insurance.  We find evidence that several factors are important in explaining the purchase of both kinds of insurance including income, wealth, and the form of the legal system.

Recently compiled OECD data, which reports insurance premiums on a "by line basis," were analyzed. The data span twenty-two countries and seven years, 1987-1993.The analysis employs panel data and ordinary least squares regression techniques.

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