Description: Annual reports of the U.S. Social Security Trustees present 75-year financial projections of the system under three different deterministic sets of economic and demographic assumptions or scenarios. The extent of the divergence between these scenarios provides useful information concerning the range of possible outcomes, but, in the absence of stochastic model projections, no probability measure can be assigned to the three scenarios, apart from being described as intermediate, low-cost and high-cost. Demographic research and stochastic model forecasts of U.S. population suggest plausible hypotheses for analysis of the divergence characteristics of the actuarial solvency ratios implied by the three deterministic scenarios. Available data from the 2002 Trustees’ report are presented and various statistical measures are developed to aid in the assessment of plausible associated probability measures for the scenario projections.

Description: This paper incorporates a jump-diffusion process into the original Lee-Carter model, and uses it to forecast mortality rates and analyze mortality securitization.

Description: This paper presents a model is which can be used for certain annuities when interest rates and future lifetimes are random. These can be used in determining contingency reserves for possible adverse interest and mortality experience for collections of life annuity contracts. Certain boundary crossing probabilities for the stochastic process component of the model are obtained. From Actuarial Research Clearing House 1991, VOL. 1.

Description: This report describes a stochastic simulation approach used to estimate the amount of a level-payment annuity payable as long as the person is alive and living in his/her house. A discussion of the paper follows. From Transactions of Society of Actuaries 1991, Vol. 43.

Description: This report is sponsored by the Society of Actuaries in collaboration with Ernst & Young. It examines the application of stochastic modeling techniques to non-market risks facing the life insurance industry.

Description: This paper discusses the binominal financial and insurance models. In addition, the paper expands the discussion to the martingale probabilities measures for insurances, annuities, endowment insurances, and equity-linked products.

Description: In computing actuarial measurements, such as the moments of present value functions for insurance and annuities, the stochastic nature of the interest rate is commonly ignored. This paper treats the interest rate as a normal random variable and presents general formulas for the mean and variance of the present value function for insurance and annuities. An example demonstrating these formulas is presented. It is found that taking the force of interest to be fixed at a mean value results in slightly underestimating the actuarial present value along with the variance for both insurance and annuities.

Description: Many seniors who own houses in the United States have most of their wealth in their houses. Home Equity Conversion Mortgages are designed to allow seniors to borrow money against their house. This paper describes a stochastic simulation approach used to estimate the amount of a level-payment annuity payable as long as the senior is alive and living in his/her home. From Actuarial Research Clearing House 1990, VOL. 2.

Description: Several previous papers treat the rate of interest as a stochastic process in the determination of values of insurances and annuity functions. None of these papers consider the current interest rate as a starting point in the model. In this paper, autoregressive interest models, which are conditional upon current and past interest rates, are developed. It is shown how these models may be applied to the evaluation of moments of interest, insurance and annuity functions. Numerical results are also given.

Description: This paper proposes the use of stochastic compartment model methods for estimating both the current direct and current indirect costs of specific cancers and for forecasting future direct and indirect costs. From Transactions of Society of Actuaries 1982, Vol. 34.