Mortality-dependent financial risk measures. (English) Zbl 1168.91411

Summary: This paper uses a recently developed two-factor stochastic mortality model to estimate financial risk measures for four illustrative types of mortality-dependent financial position: investments in zero-coupon longevity bonds; investments in longevity bonds that pay annual survivor-dependent coupons; and two examples of an insurer’s annuity book that are each hedged by a longevity bond, one based on the annuity book and hedge having the same reference cohort, and the other not. The risk measures estimated are the value-at-risk, the expected shortfall and a spectral risk measure based on an exponential risk-aversion function. Results are reported on a model calibrated on data provided by the UK Government Actuary’s Department, both with and without underlying parameter uncertainty.


91B30 Risk theory, insurance (MSC2010)
91B82 Statistical methods; economic indices and measures
91B28 Finance etc. (MSC2000)
62P05 Applications of statistics to actuarial sciences and financial mathematics


Full Text: DOI


[1] Acerbi, C., Coherent representations of subjective risk aversion, (), 147-207
[2] Benjamin, B.; Pollard, J.H., The analysis of mortality and other actuarial statistics, (1993), Institute of Actuaries London
[3] Blake, D.; Burrows, W., Survivor bonds: helping to hedge mortality risk, Journal of risk and insurance, 68, 339-348, (2001)
[4] Cairns, A.J.G., Blake, D., Dowd, K., 2006a. Pricing death: frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin, in press. · Zbl 1162.91403
[5] Cairns, A.J.G., Blake, D., Dowd, K., 2006b. A two-factor model of stochastic mortality. Journal of Risk and Insurance, in press. · Zbl 1162.91403
[6] Dahl, M., Stochastic mortality in life insurance: market reserves and mortality-linked insurance products, Insurance: mathematics and economics, 35, 113-136, (2004) · Zbl 1075.62095
[7] Dowd, K., Measuring market risk, (2005), Wiley Chichester
[8] Dowd, K., Blake, D., Cairns, A.J.G., Dawson, P.E., 2006. Survivor swaps. Journal of Risk and Insurance, in press.
[9] Lin, Y.; Cox, S.H., Natural hedging of life and annuity mortality risks, (2004), Georgia State University, mimeo
[10] Lin, Y.; Cox, S.H., Securitization of mortality risks in life annuities, Journal of risk and insurance, 72, 227-252, (2005)
[11] Lin, Y., Cox, S.H., 2005b. A mortality securitization model. Working Paper. Georgia State University.
[12] Milevsky, M.A.; Promislow, S.D., Mortality derivatives and the option to annuitize, Insurance: mathematics and economics, 29, 299-318, (2001) · Zbl 1074.62530
[13] Perks, W., On some experiments in the graduation of mortality statistics, Journal of the institute of actuaries, 63, 12-57, (1932)
[14] Wang, S., Premium calculation by transforming the layer premium density, ASTIN bulletin, 26, 71-92, (1996)
[15] Wang, S., A class of distortion operations for pricing financial and insurance risks, Journal of risk and insurance, 67, 15-36, (2000)
[16] Yang, S., 2001. Reserving, pricing and hedging for guaranteed annuity options. Ph.D. Thesis. Heriot-Watt University.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.