A dynamic equivalence principle for systematic longevity risk management. (English) Zbl 1411.91283

Summary: This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the law of large numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders.


91B30 Risk theory, insurance (MSC2010)
Full Text: DOI Link


[1] Blake, D.; Cairns, A.; Coughlan, G.; Dowd, K.; MacMinn, R., The new life market, J. Risk Insurance, 80, 501-557, (2013)
[2] Blake, D.; El Karoui, N.; Loisel, S.; MacMinn, R., Longevity risk and capital markets: the 2015-16 update, Insurance Math. Econom., (2017)
[3] Boon, L.-N., Briere, M., Werker, B., 2018. Longevity risk: To bear or to insure?, https://papers.ssrn.com/sol3/papers.cfm?abstractid=2926902.
[4] Chen, A., Hieber, P., Klein, J., 2017. Tonuity: A Novel Individual-Oriented Retirement Plan, Available at SSRN: https://ssrn.com/abstract=3043013.
[5] Cox, S.; Lin, Y., Natural hedging of life and annuity mortality risks, N. Am. Actuar. J., 11, 1-15, (2007)
[6] Dahl, M., Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts, Insurance Math. Econom., 35, 113-136, (2004) · Zbl 1075.62095
[7] Denuit, M.; Dhaene, J.; Goovaerts, M.; Kaas, R., Actuarial Theory for Dependent Risks: Measures, Orders and Models, (2005), Wiley
[8] Denuit, M.; Dhaene, J.; Hanbali, H.; Lucas, N.; Trufin, J., Updating mechanism for lifelong insurance contracts subject to medical inflation, Eur. Actuar. J., 7, 133-163, (2017) · Zbl 1394.91208
[9] Denuit, M.; Haberman, S.; Renshaw, A., Longevity-indexed life annuities, N. Am. Actuar. J., 15, 97-111, (2011) · Zbl 1213.91088
[10] Dhaene, J.; Godecharle, E.; Antonio, K.; Denuit, M.; Hanbali, H., Lifelong health insurance covers with surrender values: updating mechanisms in the presence of medical inflation, Astin Bull., 47, 803-836, (2017) · Zbl 1390.91176
[11] Feng, R.; Shimizu, Y., Applications of central limit theorems for equity-linked insurance, Insurance Math. Econom., 69, 138-148, (2016) · Zbl 1369.91082
[12] Forman, J. B.; Sabin, M. J., Survivor funds, Pace Law Rev., 37, (2016)
[13] Kaas, R.; Goovaerts, M.; Dhaene, J.; Denuit, M., Model Actuarial Risk Theory Using R, (2008), Springer · Zbl 1148.91027
[14] Luciano, E.; Regis, L.; Vigna, E., Single- and cross-generation natural hedging of longevity and financial risk, J. Risk Insurance, 84, 961-986, (2017)
[15] Majrek, D.; Nowak, W.; Ziba, W. L., Conditional strong law of large number, Int. J. Pure Appl. Math., 20, 143-157, (2005)
[16] Mauer, R.; Mitchell, O. S.; Rogalla, R.; Kartashov, V., Lifecycle portfolio choice with systematic longevity risk and variable investment-linked deferred annuities, J. Risk Insurance, 80, 649-676, (2013)
[17] Milevsky, M.; Promislow, S.; Young, V., Killing the law of large numbers: mortality risk premiums and the sharpe ratio, J. Risk Insurance, 73, 673-686, (2006)
[18] Milevsky, M.; Salisbury, T., Equitable retirement income tontines: mixing cohorts without discriminating, Astin Bull., 46, 571-604, (2016) · Zbl 1390.91201
[19] Piggott, J.; Valdez, E.; Detzel, B., The simple analytics of a pooled annuity fund, J. Risk Insurance, 72, 497-520, (2005)
[20] Pitacco, E.; Denuit, M.; Haberman, S.; Olivieri, A., Modelling Longevity Dynamics for Pensions and Annuity Business, (2009), Oxford University Press · Zbl 1163.91005
[21] Richter, A.; Frederik, W., Mortality-indexed annuities: managing longevity risk via product design, N. Am. Actuar. J., 15, 212-236, (2011)
[22] Valdez, E.; Piggott, J.; Wang, L., Demand and adverse selection in a pooled annuity fund, Insurance Math. Econom., 39, 251-266, (2006) · Zbl 1098.91078
[23] Weale, M.; van de Ven, J., Variable annuities and aggregate mortalityrisk, Natl. Inst. Econ. Rev., 237, 5561, (2016)
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.