Description: This paper studies the statistical theory underlying minimum surplus required to protect a group insurer from the insurance, or C2, risk. Followed by 2 submitted discussion papers

Description: This paper examines tandem levels of salary and interest rates and finds that the absolute level of each assumption as well as the differential are significant cost determinants for defined benefit pension plans. In forming best-estimate salary and interest rate assumptions, the actuary must reconcile the difference, if any, between the currently observed rates and the valuation assumptions. Common practice is to choose expected long-term rather than observed rates for valuation purposes. The error in this procedure is analyzed and found to be tolerable for strictly temporary discrepancies between observed rates and valuation assumptions. For situations where these discrepancies are expected to persist for some time, a need is shown for nonuniform, calendar-year assumptions or their equivalent in order to develop best-estimate assumptions. Followed by several discussion papers submitted

Description: This paper presents the general notion of a periodogram, following Elphinstone's approach. The paper then goes on to examine symmetric linear operators and their periodograms in preparation for the end discussion of periodograms of graduators.

Description: The insurance reserve for an individual contract can be pictured as a quantity which changes continuously from moment to moment in response to the forces of interest and mortality. A different mathematical model arises for each method of defining the death benefit, and in this paper a number of such mathematical models are analyzed. Followed by discussion papers submitted by several authors

Description: This paper focuses on the fact that life and annuity reserves that are determined from discounted case flows mask the dynamic nature of interest rates. To study this effect in a stochastic interest environment, the authors look at a change in discounted reserves. By looking at the appropriate measure of change, the paper explores potential short-term consequences of changes in the interest environment.

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: 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: In this paper, we propose measures of the risk that the value of the liabilities becomes larger than the value of the assets, and this especially for insurance companies. We study probabilities of mismatching and a degree of mismatching in unsegmented and multidimensional models of the balance, in which we stress the influence of interest rates on the active and passive side of the balance.