Optimal longevity risk transfer and investment strategies. (English) Zbl 1465.91093

The paper focus on relevant problems affecting pension plans, because of market downturns, low interest rates, increasing life expectancies, and new pension accounting standards. One of the most burning issues arises from managing longevity risk. This study is specifically aimed at the management of longevity risk; for this purpose, the authors formalize a model that also takes into account factors such as asset investment risk and regulatory constraints. After introducing the mortality model and the market price of longevity risk, the authors derive the price of annuity contracts sold by an insurer and model the dynamics of its investments and surplus. Then, the optimization framework for longevity risk transfer with reinsurance is described. Moreover, having observed that the capital market offers better solutions to cope with longevity risk, in terms of capital availability, the authors introduce longevity risk management with capital market solutions. In particular, the optimal longevity risk transfer decision with reinsurance and a longevity bond is treated. Numerical evidences show the practical feasibility of the model.


91G05 Actuarial mathematics
Full Text: DOI


[1] ARTEMIS (2014)
[2] Beliaeva, N. A., G. M. Soto, S. K. Nawalkha, and I. Ismailescu. 2007. Dynamic term structure modeling: The fixed income valuation course. New York: Wiley.
[3] Cairns, A. J.; Blake, D.; Dowd., K., Pricing death: Frameworks for the valuation and securitization of mortality risk, ASTIN Bulletin, 36, 1, 79-120 (2006) · Zbl 1162.91403
[4] Cairns, A. J.; Blake, D.; Dowd., K., Modelling and management of mortality risk: A review, Scandinavian Actuarial Journal, 2008, 2-3, 79-113 (2008) · Zbl 1224.91048
[5] Collin-Dufresne, P.2004 (June). Affine term structure models I: Term-premia and stochastic volatility. UC Berkeley, lectures given at Copenhagen Business School.
[6] Cox, J. C.; Huang., C. F., Optimal consumption and portfolio policies when asset prices follow a diffusion process, Journal of Economic Theory, 49, 33-83 (1989) · Zbl 0678.90011
[7] Cox, J. C.; Ingersoll, J. E. Jr.; Ross., S. A., A theory of the term structure of interest rates, Econometrica, 385-407 (1985) · Zbl 1274.91447
[8] Cox, S. H.; Lin., Y., Natural hedging of life and annuity mortality risks, North American Actuarial Journal, 11, 3, 1-15 (2007)
[9] Cox, S. H.; Lin, Y.; Petersen., H., Mortality risk modeling: Applications to insurance securitization, Insurance: Mathematics and Economics, 46, 1, 242-53 (2010) · Zbl 1231.91168
[10] Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga., L. F., Mortality portfolio risk management, Journal of Risk and Insurance, 80, 4, 853-90 (2013)
[11] Cox, S. H.; Lin, Y.; Wang., S., Multivariate exponential tilting and pricing implications for mortality securitization, Journal of Risk and Insurance, 73, 4, 719-36 (2006)
[12] Cummins, J. D.; Trainar., P., Securitization, insurance, and reinsurance, Journal of Risk and Insurance, 76, 3, 463-92 (2009)
[13] Cvitanic, J.; Karatzas., I., Convex duality in constrained portfolio optimization, The Annals of Applied Probability, 2, 4, 767-818 (1992) · Zbl 0770.90002
[14] Dahl, M.; Møller., T., Valuation and hedging of life insurance liabilities with systematic mortality risk, Insurance: Mathematics and Economics, 39, 2, 193-217 (2006) · Zbl 1201.91089
[15] Duffie, D., Dynamic asset pricing theory (2001), Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 1140.91041
[16] Ekeland, I.; Taflin, E., A theory of bond portfolios, The Annals of Applied Probability, 15, 2, 1260-1305 (2005) · Zbl 1125.91051
[17] Hakansson, N. H., Optimal investment and consumption strategies under risk for a class of utility functions, Econometrica, 587-607 (1970) · Zbl 0205.48902
[18] Halkias, M. (2015)
[19] Hull, J.; White., A., Pricing interest-rate-derivative securities, Review of Financial Studies, 3, 4, 573-92 (1990) · Zbl 1386.91152
[20] Karatzas, I.; Lehoczky, J. P.; Shreve., S. E., Optimal portfolio and consumption decisions for a “small investor” on a finite horizon, SIAM Journal of Control and Optimization, 25, 6, 1557-86 (1987) · Zbl 0644.93066
[21] Karatzas, I.; Shreve, S., Brownian motion and stochastic calculus, 113 (1991), Springer Science & Business Media · Zbl 0734.60060
[22] Korn, R.; Kraft., H., A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40, 4, 1250-69 (2002) · Zbl 1020.93029
[24] Lin, Y.; Cox., S. H., Securitization of mortality risks in life annuities, Journal of Risk and Insurance, 72, 2, 227-52 (2005)
[25] Lin, Y.; Liu, S.; Yu., J., Pricing mortality securities with correlated mortality indices, Journal of Risk and Insurance, 80, 4, 921-48 (2013)
[26] Lin, Y.; MacMinn, R. D.; Tian., R., De-risking defined benefit plans, Insurance: Mathematics and Economics, 63, 52-65 (2015) · Zbl 1348.91170
[27] Lin, Y., R. D. MacMinn, R. Tian, and J. Yu. 2017. Pension risk management in the enterprise risk management framework. Journal of Risk and Insurance, 84: 345-65.
[28] Lin, Y.; Shi, T.; Arik., A., Pricing buy-ins and buy-outs, Journal of Risk and Insurance, 84, 367-92 (2017)
[29] Lin, Y.; Tan, K. S.; Tian, R.; Yu., J., Downside risk management of a defined benefit plan considering longevity basis risk, North American Actuarial Journal, 18, 1, 68-86 (2014) · Zbl 1412.91048
[30] Loubergé, H.; Kellezi, E.; Gilli., M., Using catastrophe-linked securities to diversify insurance risk: A financial analysis of cat bonds, Journal of Insurance Issues, 22, 2, 125-46 (1999)
[31] Merton, R. C., Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51, 247-57 (1969)
[32] Pension Insurance Corporation (2015)
[33] Pulley, L. B., Mean-variance approximations to expected logarithmic utility, Operations Research, 31, 685-96 (1983)
[34] Rockafellar, R. T., Convex analysis (1970), Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 0202.14303
[35] Rogers, L. C. G., The relaxed investor and parameter uncertainty, Finance and Stochastics, 5, 2, 131-54 (2001) · Zbl 0993.91017
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.