##
**Downside risk management of a defined benefit plan considering longevity basis risk.**
*(English)*
Zbl 1412.91048

Summary: To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

PDF
BibTeX
XML
Cite

\textit{Y. Lin} et al., N. Am. Actuar. J. 18, No. 1, 68--86 (2014; Zbl 1412.91048)

Full Text:
DOI

### References:

[1] | Blake, D.; Cairns, A. J. G.; Dowd, K., Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities, British Actuarial Journal, 12, 153-197, (2006) |

[2] | Blake, D.; Cairns, A. J. G.; Dowd, K.; MacMinn, R., Longevity Bonds: Financial Engineering, Valuation, and Hedging, Journal of Risk and Insurance, 73, 647-672, (2006) |

[3] | Bogentoft, E.; Romeijn, H. E.; Uryasev, S., Asset/Liability Management for Pension Funds Using CVaR Constraints, Journal of Risk Finance, 3, 57-71, (2001) |

[4] | Brcic, J.; Brisebois, C., An Age-Old Story, (2010) |

[5] | Cairns, A. J., Modelling and Management of Longevity Risk: Approximations to Survivor Functions and Dynamic Hedging, Insurance: Mathematics and Economics, 49, 438-453, (2011) · Zbl 1230.91068 |

[6] | Cairns, A. J. G.; Blake, D.; Dowd, K., Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk, ASTIN Bulletin, 36, 79-120, (2006) · Zbl 1162.91403 |

[7] | Carter, L. R.; Lee, R. D., Modeling and Forecasting Us Sex Differentials in Mortality, International Journal of Forecasting, 8, 35-45, (1992) |

[8] | Chang, S. C.; Tzeng, L. Y.; Miao, J. C., Pension Funding Incorporating Downside Risks, Insurance: Mathematics and Economics, 32, 217-228, (2003) · Zbl 1074.91547 |

[9] | Colombo, L.; Haberman, S., Optimal Contributions in a Defined Benefit Pension Scheme with Stochastic New Entrants, Insurance: Mathematics and Economics, 37, 335-354, (2005) · Zbl 1117.91380 |

[10] | A Report on the Economic Regulation of the London Airports companies (Heathrow Airport Ltd and Gatwick Airport Ltd), (2007) |

[11] | Coughlan, G.; Epstein, D.; Sinha, A.; Honig, P., q-forwards: Derivatives for Transferring Longevity and Mortality Risk, (2007) |

[12] | Coughlan, G.; Khalaf-Allah, M.; Ye, Y.; Kumar, S.; Cairns, A.; Blake, D.; Dowd, K., Longevity Hedging 101: A Framework for Longevity Basis Risk Analysis and Hedge Effectiveness, North American Actuarial Journal, 15, 150-176, (2011) |

[13] | Cowling, C.; Dales, R., The FTSE 100 and Their Pension Disclosures, (2008) |

[14] | Cox, S. H.; Lin, Y., Natural Hedging of Life and Annuity Mortality Risks, North American Actuarial Journal, 11, 1-15, (2007) |

[15] | Cox, S. H.; Lin, Y.; Petersen, H., Mortality Risk Modeling: Applications to Insurance Securitization, Insurance: Mathematics and Economics, 46, 242-253, (2010) · Zbl 1231.91168 |

[16] | Cox, S. H.; Lin, Y.; Tian, R.; Yu, J., Managing Capital Market and Longevity Risks in a Defined Benefit Pension Plan, Journal of Risk and Insurance, 80, 585-619, (2013) |

[17] | Cox, S. H.; Lin, Y.; Tian, R.; Zuluaga, L. F., Mortality Portfolio Risk Management, Journal of Risk and Insurance., (2012) |

[18] | Cox, S. H.; Lin, Y.; Wang, S., Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization, Journal of Risk and Insurance, 73, 719-736, (2006) |

[19] | Delong, Ł.; Gerrard, R.; Haberman, S., Mean-Variance Optimization Problems for an Accumulation Phase in a Defined Benefit Plan, Insurance: Mathematics and Economics, 42, 107-118, (2008) · Zbl 1141.91501 |

[20] | Haberman, S., Stochastic Investment Returns and Contribution Rate Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, 19, 127-139, (1997) · Zbl 0901.90012 |

[21] | Haberman, S.; Butt, Z.; Megaloudi, C., Contribution and Solvency Risk in a Defined Benefit Pension Scheme, Insurance: Mathematics and Economics, 27, 237-259, (2000) · Zbl 0994.91030 |

[22] | Habermana, S.; Sung, J.-H., Optimal Pension Funding Dynamics Over Infinite Control Horizon When Stochastic Rates of Return Are Stationary, Insurance: Mathematics and Economics, 36, 103-116, (2005) · Zbl 1111.91023 |

[23] | Josa-Fombellida, R.; Rincón-Zapatero, J. P., Optimal Risk Management in Defined Benefit Stochastic Pension Funds, Insurance: Mathematics and Economics, 34, 489-503, (2004) · Zbl 1188.91202 |

[24] | Josa-Fombellida, R.; Rincón-Zapatero, J. P., Optimal Investment Decisions with a Liability: The Case of Defined Benefit Pension Plans, Insurance: Mathematics and Economics, 39, 81-98, (2006) · Zbl 1147.91341 |

[25] | Kouwenberg, R., Scenario Generation and Stochastic Programming Models for Asset Liability Management, European Journal of Operational Research, 34, 279-292, (2001) · Zbl 1008.91050 |

[26] | Li, J. S.-H.; Hardy, M. R., Measuring Basis Risk in Longevity Hedges, North American Actuarial Journal, 15, 177-200, (2011) · Zbl 1228.91042 |

[27] | Li, N.; Lee, R., Coherent Mortality Forecasts for a Group of Population: An Extension of the Lee-Carter Method, Demography, 42, 575-594, (2005) |

[28] | Lin, Y.; Cox, S. H., Securitization of Mortality Risks in Life Annuities, Journal of Risk and Insurance, 72, 227-252, (2005) |

[29] | Lin, Y.; Cox, S. H., Securitization of Catastrophe Mortality Risks, Insurance: Mathematics and Economics, 42, 628-637, (2008) · Zbl 1152.91593 |

[30] | Lin, Y.; Liu, S.; Yu, J., Pricing Mortality Securities with Correlated Mortality Indices, Journal of Risk and Insurance, (2012) |

[31] | Loeys, J.; Panigirtzoglou, N.; Ribeiro, R. M., Longevity: A Market in the Making, (2007) |

[32] | 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: Mathematics and Economics, 45, 25-34, (2009) · Zbl 1231.91216 |

[33] | Milidonis, A.; Lin, Y.; Cox, S. H., Mortality Regimes and Pricing, North American Actuarial Journal, 15, 266-289, (2011) · Zbl 1228.91043 |

[34] | Ngwira, B.; Gerrard, R., Stochastic Pension Fund Control in the Presence of Poisson Jumps, Insurance: Mathematics and Economics, 40, 283-292, (2007) · Zbl 1120.60063 |

[35] | Owadally, M.; Habermana, S., Efficient Amortization of Actuarial Gains/Losses and Optimal Funding in Pension Plans, North American Actuarial Journal, 8, 21-36, (2004) · Zbl 1085.62509 |

[36] | Plat, R., Stochastic Portfolio Specific Mortality and the Quantification of Mortality Basis Risk, Insurance: Mathematics and Economics, 45, 123-132, (2009) · Zbl 1231.91226 |

[37] | Rockafellar, R. T.; Uryasev, S., Optimization of Conditional Value-at-Risk, Journal of Risk, 2, 21-41, (2000) |

[38] | Sheikh, A. Z.; Sun, J., The Blind Side: Managing Downside Risk in Corporate Defined Benefit Plans, (2010) |

[39] | Sherris, M.; Wills, S., Financial Innovation and the Hedging of Longevity Risk, Asia-Pacific Journal of Risk and Insurance, 3, 52-64, (2008) |

[40] | World Populations Prospects: The 1996 Revision, (1998), New York, United Nations: Population Division, New York, United Nations |

[41] | Tian, R.; Cox, S. H.; Lin, Y.; Zuluaga, L., Portfolio Risk Management with CVaR-like Constraints, North American Actuarial Journal, 14, 86-106, (2010) · Zbl 1219.91132 |

[42] | Tsai, J. T.; Wang, J. L.; Tzeng, L. Y., On the Optimal Product Mix in Life Insurance Companies Using Conditional Value at Risk, Insurance: Mathematics and Economics, 235-241, (2010) · Zbl 1231.91244 |

[43] | White, K. M., Longevity Advances in High-Income Countries, 1955–96, Population and Development Review, 59-76, (2002) |

[44] | Wills, S.; Sherris, M., Securitization, Structuring and Pricing of Longevity Risk, Insurance: Mathematics and Economics, 46, 173-185, (2010) · Zbl 1231.91251 |

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.