Description: 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 rnodel.

Description: The Annual Reports of the Trustees, for the Social Security Trust Funds, are cornucopia of data. However, the major focus is on projections expressed as a percentage of payroll. The purpose of this paper is to suggest that additional measures - which would supplement, rather than replace the percentage of payroll data - should be examined to evaluate the projected effect of the cash benefits OASDI program.

Description: There are three commonly used methods for compiling exposure and death data for use in obtaining crude mortality rates. They are lives, policies and amounts of insurance. This paper investigates the properties of estimators based on lives, amounts and robust alternatives. It is concluded that lives provide the best estimator, even when there is a moderate dependence of mortality rates on amounts of insurance. Presented at the Fourteenth Actuarial Research Conference, lowa City, lowa, September 6, 1979.

Description: This is a Fellowship Credit Research Paper. A portfolio of different insurance policies such as temporary, endowment and whole-life insurance policies is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results.

Description: This paper is to some extent a sequel to my previous paper A Bond Manager's Method for ALM published in Actuarial Research Clearing House Volume 1993.3. It borrows from that paper the concept of benchmark weights for measuring the sensitivity of the present value of a set of cash flows to changes in interest rates. However, a completely different approach to calculating benchmark weights is presented.

Description: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.

Description: The purpose of this paper is to introduce the use of least squares for estimating parameters of mortality curves and discuss the advantages of this method.

Description: The initial risk reserves in collective risk models vary according to the underlying claim distribution, and a suitable level of ruin probability. A thorough analysis of the needed initial surplus for various ruin probability levels is provided in eight meaningful examples. The claim distributions are drawn from various fields of insurance, including property damage and liability insurance.

Description: The purpose of this note is to show how certain formulas of life contingencies can be derived almost painlessly under the uniform distribution of deaths assumption.

Description: In this paper we discuss the link between the price of a contingent claim and its replicating strategies. We compute the replicating strategies for some contingent claims when the price of stocks are modeled using either the Wiener process or the Poisson process. These replicating strategies are essential knowledge if one wishes to implement a dynamic trading strategy.