Author’s Reply: Statistical Independence and Fractional Age Assumptions - Discussion by Cecil Nesbitt; Elias S. W. Shiu; Serena Tiong,January 1997

Abstract

This paper addresses the problem of the sharing of longevity risk between an annuity provider and a group of annuitants. An appropriate longevity index is designed in order to adapt the amount of the periodic payments in life annuity contracts. This accounts for unexpected longevity improvements experienced by a given reference population. The approach described in the present paper is in contrast with group self-annuitization, where annuitants bear their own risk. Here the annuitants bear only the nondiversifiable risk that the future mortality trend departs from that of the reference forecast. In that respect, the life annuities discussed in this paper are substitutes for reinsurance and securitization of longevity risk.     

“Actuarial Issues in the Novels of Jane Austen”, Daniel D. Skwire,January 1997

Social security systems for old age have been explicitly studied in a public choice framework for more than 30 years. They illustrate extremely well the problems of allocating economic resources through a system of voting. Despite actuarial interest in state pension systems and despite the actuarial calculations that are needed to understand long-term public choice trends, there is almost no reference to public choice economics in the actuarial pensions literature. It can be argued that pension systems currently provide some of the most significant threats to the long-term budget positions of developed countries, a point that was made in the Nobel Laureate lecture of Professor James Buchanan over 24 years ago. In this article, we look at the costs and benefits that will be faced by different groups of voters as a result of state pension reform in the United Kingdom. The results of this analysis suggest that a majority of the electorate will have a strong financial interest in opposing state pension reform except where reform involves raising retirement ages. These results are in accordance not just with theoretical work but with other empirical work and practical observations.     

“The Future of Risk Classification in the Age of Predictive DNA-Based Testing”, Donald C. Chambers,January 1999

Abstract

The correlation among multiple lines of business plays an important role in quantifying the uncertainty of loss reserves for insurance portfolios. To accommodate correlation, most multivariate loss-reserving methods focus on the pairwise association between corresponding cells in multiple run-off triangles. However, such practice usually relies on the independence assumption across accident years and ignores the calendar year effects that could affect all open claims simultaneously and induce dependencies among loss triangles. To address this issue, we study a Bayesian log-normal model in the prediction of outstanding claims for dependent lines of business. In addition to the pairwise correlation, our method allows for an explicit examination of the correlation due to common calendar year effects. Further, different specifications of the calendar year trend are considered to reflect valuation actuaries’ prior knowledge of claim development. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer. It is shown that the incorporation of calendar year effects improves model fit significantly, though it contributes substantively to the predictive variability. The availability of the realizations of predicted claims permits us to perform a retrospective test, which suggests that extra prediction uncertainty is indispensable in modern risk management practices.