Description: This report looks at closed form models or 'exact solutions' in which calculus produces 'simple' formulae. The conclusion is that for Gaussian interest rate models we can solve the problem of an American option provided the option holder behaviour can be described by a force of option exercise which is linear or quadratic in the state variables.

Description: This paper presents a proof using the general mean value theorem that under specified conditions, the insurance premium for complete protection against a specified loss will decrease with increasing wealth. From Actuarial Research Clearing House 1994, Vol. 1.

Description: The financing for Social Security is a pay-as-you-go system, rather than the full-reserve system utilized in private insurance, and the financing conditions of the trust funds have more uncertainty than does the reserve in private insurance. Traditionally, the financing conditions have been decided by a deterministic approach using economic and demographic assumptions that rely upon negotiation among experts at various government agencies. This paper proposes an econometric approach, called the 'co-integrated multivariate time series model,' for forecasting the financing conditions of the trust funds. This stochastic approach not only establishes the interrelationships but also clarifies the co-movements among the economic assumptions. Furthermore, it helps analyze the original assumptions rather than the differences of the nonstationary assumption variables adopted by researchers in the past that are more difficult to interpret. Use of this approach permits the assessment of the probability distribution of the future balance of trust funds instead of assessing estimates from the three alternative deterministic assumptions. This distribution will provide policy-makers with a better assessment of stability of the trust funds.

Description: Letters to the national association of insurance commissioners life/health actuarial task force regarding the development of the new annuity non-forfeiture law. Letters are addressed to Mr. Howard Kayton, Mr. Allan Roby, and Mr. John Montgomery. Also included is a demonstration of the workings of a two tiered annuity.

Description: This paper suggests ways of presenting ideas from the theory of compound interest and actuarial mathematics using simulation on spreadsheets. From the Actuarial Research Clearing House 1997 Vol. 1.

Description: It is assumed that the force of interest varies as an auto-regressive process of order 2, AR[2]. The moments of the accumulated value of 1 paid at the beginning of each period, for n periods, are developed using moment generating functions.

Description: Brief comment from the Editor about the 17th Actuarial Research Conference in 1982.

Description: The purpose of this paper is to introduce some actuarial applications of Tchebyshef's Inequality.

Description: In this paper several probability models for the random amounts of needed long-term care are explained, and one model is used to provide an alternate premium calculation method for certain long-term care coverages. From Actuarial Research Clearing House 1990, VOL. 2.

Description: This is the abstract of a paper that presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. It takes an individual approach rather than the aggregate approach used in traditional methods of analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but may later move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable 'risk level' random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained using this model.