Description: This paper represents a brief progress report on research, being sponsored by the Casualty Actuarial Society and the Society of Actuaries, in the area of modeling of economic series. In particular, research is being undertaken to provide a foundation for the actuarial community’s modeling of a variety of economic variables, including interest rates, equity returns, inflation, unemployment rates, and real estate price levels. The specific objectives of this research are to provide a summary of the literature in the area of economic scenario modeling, identify data sources and methodologies in this area useful to the actuarial profession, and produce working software for economic modeling, including appropriate documentation, to be made available to the general actuarial community in order to allow actuaries to use and build upon this research. From Actuarial Research Clearing House 2004, Vol. 1.

Description: Design and future maintenance of an asset portfolio backing a new line of business is critical for proper asset and liability management for that business. Most portfolio optimization methods utilize linear or quadratic programming and require the user to specify the asset and liability attributes and cash flows into the program. The programmer must also supply an objective function to allow the program to find the optimal asset mix for the associated liabilities. Two problems with this approach are that the liability cash flows are fairly static and that one must frequently rebalance the portfolio. An alternative approach would be to develop a corporate model of both the assets and liabilities and incorporate various economic scenarios as input into the model. Asset strategies would be measured against a specific objective function that is calculated by the corporate model. Unfortunately, the majority of maximization algorithms available are very time consuming, and obtaining a reasonable portfolio mix becomes impractical. This paper overcomes this difficulty by using a very rapid optimization method from the chemical engineering profession called the Floppy Triangle. The paper includes an example of the use of this process to determine an optimal portfolio. It also discusses modifications of the algorithm that is required when the shorting of assets is not permitted.

Description: One of the most important problems in Finance is the valuation of financial securities written on underlying assets whose prices are subject to uncertainty. This paper presents a technique to estimate the unknown stochastic volatilities by solving the inverse problem associated with the parabolic partial differential equation governing risk neutral derivative security prices. This technique can be applied in a very general multi-factor setting and numerical examples are provided.

Description: This review summarizes the key features of a stochastic model that works with non-life insurance claim incurral, accrual and reporting. More specifically it provides an overview of the claim model components, classical parameter estimators, test statistics, and forecast point estimates and error variances. From Actuarial Research Clearing House 1991, VOL. 1.

Description: This paper introduces the symbolic valuation, a stochastic valuation which allows flexible interest rate and cash flow assumptions, and provides an illustration which values a simple SPDA product. From Actuarial Research Clearing House 1992, Vol. 1.

Description: This is an Excel 2003 spreadsheet that accompanies the research report entitled 'The Effect of Deflation or High Inflation on the Insurance Industry.' It models scholastically the effects of inflation and deflation.

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 section contains multiple book reviews and notices concerning the actuarial profession. Reviews: 'Medical Risks: Patterns of Mortality and Survival' by Singer and Levinson, 'The Theory and Practice of Pension Funding' by Trowbridge and Farr, 'Two Stochastic Processes' by Beekman, 'Disability Income Insurance - Cost Differentials between Men and Women' by New York Insurance Department, 'Social Security and Private Pension Plans: Competitive or Complementary' by McGill, 'A New Look at Accounting for Pension Costs' by Hall and Landsittel, '1977 Annual Reports of the Board of Trustees of the Federal OASDI Trust Funds...,' 'Investigation of Sickness Statistics - Individual Policies, 1971 and 1973' by the Institute of Actuaries and the Faculty of Actuaries, 'The Graduation of Pensioners and of Annuitants Mortality Experience 1967-70' by the Institute of Actuaries and the Faculty of Actuaries, 'Pensions and Survival - the Coming Crisis of Money and Retirement' by Calvert, 'Group Benefits in a Changing Society' by Spencer, 'Experience of Disabled Work Benefits under OASDI 1965-74' by Bayo and Wilkin. Digests also included.

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: 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.