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: 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: Given a financial transaction we are often interested in the number of internal rates of return [yield rates] and their location. From an actuarial point of view, the fundamental question is to identify those transactions with a single yield rate, or a single rate in some interval such as the positive reals. In this paper we are concerned with this counting problem. We survey various results concerning this problem, and provide a unifying approach together with some new insights.

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: This paper presents an approach to analyzing continuing care retirement community [CCRC] data, and demonstrates the methods using data from a large CCRC. It is assumed that residents make transitions among a number of states that represent the levels of care required by residents. There is randomness associated with both the transition times and the states entered at these times. The model is conveniently characterized in terms of transition intensity functions, which represent the instantaneous rates of transition between pairs of states.

Description: This is the abstract of the paper Hedging of Insurance Contracts. ls the tinting of liabilities e.g. the IBNR case irrelevant to investment decisions in an insurance company? Even in the extreme case of independence between claim developments and movements in the financial markets, the assumption of constant insurers' absolute measure of risk aversion is necessary for a positive answer to the initial question.

Description: In a paper entitled ‘Using Cash Flows to Allocate Investment Income’ [ARCH 1979.1] reference was made to the conversion of investment rates [and capital gain and loss rates] from rates based upon periods of original contribution to rates based upon dollars of original contribution. Thus arose the topic of this note.

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.

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: This note develops the optimality of the put option as a hedging strategy. For an investor who owns a stock, he can buy a put option to hedge against the downside risk of the stock price. In this short note, we ask two questions with the hedge strategy of the put option. First, whether the investor is better off with the hedging strategy? Second, if the investor is better off with the hedging strategy, whether it is the optimal hedging plan? Our result shows that in a risk averse world an investor will maximize his utility with buying the put option as a hedge strategy.