De-risking defined benefit plans. (English) Zbl 1348.91170

Summary: To identify an appropriate pension de-risking method, this paper proposes an optimization model that minimizes the expected total pension cost subject to a conditional value at risk (CVaR) constraint on pension funding level. Using this model, we examine three pension hedging strategies, i.e., longevity hedge, buy-in and buy-out; each strategy is examined with hedging costs that include a risk premium, search and information cost, underfunding cost, and counter-party risk cost. The numerical examples demonstrate that these hedging costs have a significant impact on the hedging decision. The hedge ratio (total pension cost) decreases (increases) with the transaction cost, the counter-party default probability and the underfunding ratio. In addition, the buy-out underperforms the longevity hedge and the buy-in for underfunded plans and the longevity hedge is less sensitive to the default risk than the buy-in.


91B30 Risk theory, insurance (MSC2010)
91G70 Statistical methods; risk measures
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI


[1] Black, F., Should you use stocks to hedge your pension liability, Financ. Anal. J., 45, 1, 10-12, (1989)
[2] Blake, D.; Cairns, A. J.G.; Dowd, K., Living with mortality: longevity bonds and other mortality-linked securities, Br. Actuar. J., 12, 153-197, (2006)
[3] Bodie, Z., Instituteshortfall risk and pension fund asset management, Financ. Anal. J., 47, 3, 57-61, (1991)
[4] Bogentoft, E.; Romeijn, H. E.; Uryasev, S., Asset/liability management for pension funds using CVaR constraints, J. Risk Financ., 3, 2, 57-71, (2001)
[5] Cairns, A. J., Modelling and management of longevity risk: approximations to survivor functions and dynamic hedging, Insurance Math. Econom., 49, 438-453, (2011) · Zbl 1230.91068
[6] Chang, S. C.; Tzeng, L. Y.; Miao, J. C., Pension funding incorporating downside risks, Insurance Math. Econom., 32, 217-228, (2003) · Zbl 1074.91547
[7] Colombo, L.; Haberman, S., Optimal contributions in a defined benefit pension scheme with stochastic new entrants, Insurance Math. Econom., 37, 335-354, (2005) · Zbl 1117.91380
[8] Coughlan, G.; Blake, D.; MacMinn, R. D.; Cairns, A. J.G.; Dowd, K., Handbook of insurance, (2013), Springer Science+Business Media New York, (Chapter 34): Longevity risk and hedging solutions
[9] Cox, S. H.; Lin, Y., Natural hedging of life and annuity mortality risks, N. Am. Actuar. J., 11, 3, 1-15, (2007)
[10] Cox, S. H.; Lin, Y.; Petersen, H., Mortality risk modeling: applications to insurance securitization, Insurance Math. Econom., 46, 1, 242-253, (2010) · Zbl 1231.91168
[11] Cox, S. H.; Lin, Y.; Tian, R.; Yu, J., Managing capital market and longevity risks in a defined benefit pension plan, J. Risk Insurance, 80, 3, 585-619, (2013)
[12] Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga, L. F., Mortality portfolio risk management, J. Risk Insurance, 80, 4, 853-890, (2013)
[13] Cox, S. H.; Lin, Y.; Wang, S., Multivariate exponential tilting and pricing implications for mortality securitization, J. Risk Insurance, 73, 4, 719-736, (2006)
[14] Delong, Ł.; Gerrard, R.; Haberman, S., Mean-variance optimization problems for an accumulation phase in a defined benefit plan, Insurance Math. Econom., 42, 1, 107-118, (2008) · Zbl 1141.91501
[15] Deutsche Bank, 2011. Pension-derisking: Longevity hedging and buying out. http://cbs.db.com. Published by ClearPath Analysis.
[16] Dowd, K.; Cairns, A. J.; Blake, D., Mortality-dependent financial risk measures, Insurance Math. Econom., 38, 3, 427-440, (2006) · Zbl 1168.91411
[17] Ehrhardt, J.W., Wadia, Z., Perry, A., 2013. De-risking efforts by plan sponsors reduce pension obligations, but continued discount rate declines produce record-high pension plan deficit in 2012. www.milliman.com. Published on March 2013.
[18] Haberman, S.; Butt, Z.; Megaloudi, C., Contribution and solvency risk in a defined benefit pension scheme, Insurance Math. Econom., 27, 237-259, (2000) · Zbl 0994.91030
[19] Hamilton, D.T., Cantor, R., 2006. Measuring corporate default rates. Moody’s Investors Service.
[20] Josa-Fombellida, R.; Rincón-Zapatero, J. P., Optimal risk management in defined benefit stochastic pension funds, Insurance Math. Econom., 34, 3, 489-503, (2004) · Zbl 1188.91202
[21] Kouwenberg, R., Scenario generation and stochastic programming models for asset liability management, European J. Oper. Res., 34, 279-292, (2001) · Zbl 1008.91050
[22] LCP, 2012. LCP pension buy-ins, buy-outs and longevity swaps 2012. http://www.lcp.uk.com. Download on April 6, 2013.
[23] Lee, R. D.; Carter, L., Modelling and forecasting the time series of US mortality, J. Amer. Statist. Assoc., 87, 419, 659-671, (1992)
[24] Li, J. S.-H.; Hardy, M. R., Measuring basis risk in longevity hedges, N. Am. Actuar. J., 15, 2, 177-200, (2011) · Zbl 1228.91042
[25] Lin, Y.; Cox, S. H., Securitization of mortality risks in life annuities, J. Risk Insurance, 72, 2, 227-252, (2005)
[26] Lin, Y.; Cox, S. H., Securitization of catastrophe mortality risks, Insurance Math. Econom., 42, 2, 628-637, (2008) · Zbl 1152.91593
[27] Lin, Y.; Liu, S.; Yu, J., Pricing mortality securities with correlated mortality indices, J. Risk Insurance, 80, 4, 921-948, (2013)
[28] Lin, Y.; Tan, K. S.; Tian, R.; Yu, J., Downside risk management of a defined benefit plan considering longevity basis risk, N. Am. Actuar. J., 18, 1, 68-86, (2014) · Zbl 1412.91048
[29] Lucas, D. J.; Zeldes, S. P., How should public pension plans invest?, Amer. Econ. Rev., 99, 2, 527-532, (2009)
[30] Maurer, R.; Mitchell, O. S.; Rogalla, R., Managing contribution and capital market risk in a funded public defined benefit plan: impact of CVaR cost constraints, Insurance Math. Econom., 45, 25-34, (2009) · Zbl 1231.91216
[31] Milidonis, A.; Lin, Y.; Cox, S. H., Mortality regimes and pricing, N. Am. Actuar. J., 15, 2, 266-289, (2011) · Zbl 1228.91043
[32] Olsen, K., 2013. Pension buyouts might increase risk for plan, report finds. http://www.pionline.com. Published by Pensions & Investments.
[33] Prudential, 2012. Creating a clear path to pension plan de-risking. http://www3.prudential.com. Download on April 6, 2013.
[34] Tian, R.; Cox, S. H.; Lin, Y.; Zuluaga, L., Portfolio risk management with CVaR-like constraints, N. Am. Actuar. J., 14, 1, 86-106, (2010) · Zbl 1219.91132
[35] Vasan, P., 2011. Prudential completes first US pension buy-in transaction. http://www.ai-cio.com (Download on April 6, 2013).
[36] Vlasic, B., Walsh, M.W., 2012. G.M. plans big buyouts for retirees in pension. http://www.nytimes.com. Published on June 1, 2012.
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.