Description: The main aim of this paper is to apply some of the techniques of modern time series and econometric analysis to analyse investment data in order to better understand the nature of long run relationships in investment series typically used in stochastic investment models. The paper attempts to identify and address fundamental issues that need to be considered before developing a particular stochastic investment model.

Description: This paper presents an approach in which a defective renewal equation is solved in terms of a related compound geometric distribution. The advantage of this approach is discussed. The authors then apply this approach to a defective renewal equation which involves the time of ruin, the surplus before ruin and the total deficit at the time of ruin. They show how to compute the moments of the time of ruin as well as the joint distribution of the surplus before ruin and the deficit at the time of ruin. Two important cases in terms of claim size distributions are considered in detail. First, the authors consider exponential claim size distributions. They then consider a combination of two exponentials. The moments of the time of ruin are given in both cases.

Description: The results obtained during the last one-third of the research project and the project at whole are presented. The report only contains brief descriptions of the results which are placed in addendums and which are in reality copies of papers and a chapter of a book submitted for publication. Some theoretical and applied problems induced by the research are discussed.

Description: Abstract of a paper, In which we describe the method of obtaining k, by listing the underlying assumptions following Hogg and Klugman 1984. Then we calculate the variance of the estimator of k. We also present an alternative formula which will be suitable in other cases along with its variance.

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: Actuarial science is at a cross roads. Many are urging that our highly successful examination process be partially abandoned in favour of accepting university courses in a number of basic subjects. This drive is based in part on the difficulties in supporting the present system, the experience elsewhere and a misplaced confidence in the quality of the university system. This paper explores where the university system is and where it needs to go in order to adequately serve the interests of the actuarial community.

Description: The purpose of this paper is to trace the change in Canadian company expenses, comparing the six postwar years 1946 to 1951 with the prewar year 1939. Includes costs per policy and as percentage of premium, and also compares to expected costs. Expenses by company size are also shown.

Description: The purpose of this paper is to suggest an improved method of future mortality improvement approximation, using the a-1949 Table as the basic table. Comparisons are shown between this method and other methods for annuitants.

Description: In March this year a charter for the new corporation, the College Retirement Equities Fund, was granted by the State of New York and it is expected that within a few months the Fund will begin operations as a supplement to TIAA annuities. The purpose of this paper is to describe this rather novel type of corporation, which presents some unusual and interesting actuarial problems. Comparisons of the performance of fixed annuities vs. variable annuities are provided.

Description: This section contains book reviews and summarizes recent publications: 'Rights of Creditors in Life Insurance Policies' by Schwarzschild, 'Savings Bank Life Insurance' by Johnson, 'Transferability of Public Employee Retirement Credits among Units of Government' by Advisory Commission on Intergovernmental Relations, 'State and Private Pension Schemes in the European Economic Community and the United Kingdom' by Ratcliff, 'Surplus in British Life Assurance' by Cox and Storr-Best, 'Psychiatric Insurance - Financing Short-Term Ambulatory Treatment' by Avnet. Some digests are also included.