Evaluating life expectancy evaluations. (English) Zbl 1393.91098

Bauer, Daniel; Fasano, Michael V.; Russ, Jochen; Zhu, Nan

N. Am. Actuar. J. 22, No. 2, 198-209 (2018).

Summary: The quality of life expectancy estimates is one key consideration for an investor in life settlements. The predominant metric for assessing this quality is the so-called A-to-E ratio, which relies on a comparison of the actual to the predicted number of deaths. In this article, we explain key issues with this metric: In the short run, it is subject to estimation uncertainty for small and moderately sized portfolios; and, more critically, in the long run, it converges to 100% even if the underwriting is systematically biased. As an alternative, we propose and discuss a set of new metrics based on the difference in (temporary) life expectancies. We examine the underwriting quality of a leading U.S. life expectancy provider based on this new methodology.

MSC:

91B30

Risk theory, insurance (MSC2010)

Keywords:

life expectancy; A-to-E ratio

References:

[1]	Life settlements mortality, (2013)
[2]	Aspinwall, J.; Chaplin, G.; Venn, M., Life Settlements and Longevity Structures: Pricing and Risk, (2009), John Wiley and Sons, New York
[3]	Behan, D. F., Measurement of incurred but unreported deaths in life settlements, (2012)
[4]	Bhuyan, V. B., Life Markets: Trading Mortality and Longevity Risk with Life Settlements and Linked Securities, (2009), John Wiley and Sons, New York
[5]	Billingsley, P., Probability and Measure, (1995), John Wiley and Sons, New York · Zbl 0822.60002
[6]	Bowers, N. L.; Gerber, H. U.; Hickman, J. C.; Jones, D. A.; Nesbitt, C. J., Actuarial Mathematics, (1997), Society of Actuaries, Schaumburg, IL
[7]	Braun, A.; Gatzert, N.; Schmeiser, H., Performance and risks of open-end life settlement funds, Journal of Risk and Insurance, 79, 193-230, (2012)
[8]	Cook, D.; Ezell, G., Life settlement characteristics and mortality experience for two providers, (2008)
[9]	Davó, N. B.; Mendoza Resco, C.; Monjas Barroso, M., Portfolio diversification with life settlements: an empirical analysis applied to mutual funds, Geneva Papers on Risk and Insurance—Issues and Practice, 38, 22-42, (2013)
[10]	Gatzert, N., The secondary market for life insurance in the U.K., Germany, and the U.S.: comparison and overview, Risk Management and Insurance Review, 13, 279-301, (2010)
[11]	Giaccotto, C.; Golec, J.; Schmutz, B. P., Measuring the performance of the secondary market for life insurance policies, Journal of Risk and Insurance, 84, 127-151, (2017)
[12]	Januário, A. V.; Naik, N. Y., Testing for adverse selection in life settlements: the secondary market for life insurance policies, (2016)
[13]	Qureshi, A. H.; Fasano, M. V., Measuring actual to expected accuracy for life settlement underwriting, Reinsurance News, 68, 23-26, (2010)
[14]	Rhodes, T. E.; Freitas, S. A., Advanced statistical analysis of mortality, (2004)
[15]	Seligman, E. J.; Kahn, S., Testing for significant differences between actual and expected results, Transactions of Society of Actuaries, 32, 585-600, (1980)
[16]	Stone, C. A.; Zissu, A., Securitization of senior life settlements: managing extension risk, Journal of Derivatives, 13, 66-72, (2006)