Alternative Strategies to Hedge Longevity Risk in Defined Contribution Pension Plans for Loss-Averse Individuals

Öz

This study aims to determine the optimal investment strategy in defined contribution pension plans by extending beyond the traditional expected utility maximisation framework, and explicitly modelling investor behaviour under loss aversion to capture more realistic decision-making dynamics. While determining the optimal investment strategy for loss-averse individuals, the longevity risk arising from the decrease in mortality probabilities observed all over the world in recent years should also be considered. Accordingly, the optimal investment strategy for loss-averse individuals is derived by incorporating longevity risk into the model and employing stochastic dynamic programming as the optimisation technique. The results indicate that a loss-averse individual should follow a more aggressive investment strategy in the accumulation period to hedge longevity risk during the distribution period. Given that loss-averse individuals are generally reluctant to engage in riskier investment strategies, this study explores alternative methods to hedge longevity risk. From the results obtained, it is concluded that determining the appropriate contribution rate and the appropriate minimum fund guarantee for the loss-averse individuals reduces the risk in the optimal investment strategy. These findings underscore the importance of tailoring investment strategies in defined contribution pension plans to align with individual risk preferences and the financial challenges posed by increasing life expectancy.

Anahtar Kelimeler

• Defined contribution pension plan
• Loss aversion
• Optimal investment strategy
• Longevity risk

Kaynakça

1. Aitken, W. H. (1996). A problem-solving approach to pension funding and valuation. Actex Publications. google scholar
2. Basimanebotlhe, O., & Xue, X. (2015). Stochastic optimal investment under inflationary market with minimum guarantee for DC pension plans. Journal of Mathematics Research, 7(3), 1-15. google scholar
3. Battocchio, P., & Menoncin, F. (2004). Optimal pension management in a stochastic framework. Insurance: Mathematics and Economics, 34(1), 79-95. google scholar
4. Battocchio, P., Menoncin, F., & Scaillet, O. (2007). Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases. Annals of Operations Research, 152, 141-165. google scholar
5. Berkelaar, A. B., Kouwenberg, R., & Post, T. (2004). Optimal portfolio choice under loss aversion. Review of Economics and Statistics, 86(4), 973-987. google scholar
6. Blake, D. (1999). Annuities in pension plans. In Commentary at World Bank Annuities Workshop, 7-8 June, United Kingdom. google scholar
7. Blake, D., Cairns, A. J., & Dowd, K. (2001). Pensionmetrics: Stochastic pension plan design and value-at-risk during the accumulation phase. Insurance: Mathematics and Economics, 29(2), 187-215. google scholar
8. Blake, D., Wright, D., & Zhang, Y. (2013). Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion. Journal of Economic Dynamics and Control, 37(1), 195-209. google scholar

9. Blake, D., Wright, D., & Zhang, Y. (2014). Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners. Journal of Economic Dynamics and Control, 38, 105-124. google scholar
10. Boulier, J. F., Huang, S., & Taillard, G. (2001). Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. Insurance: Mathematics And Economics, 28(2), 173-189. google scholar
11. Cairns, A. J., Blake, D., & Dowd, K. (2006). Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics and Control, 30(5), 843-877. google scholar
12. CMIR (1999). Graduation of the 1991–94 mortality experience—the ‘‘92’’ series standard tables. Continuous Mortality Investigation Reports, 17, 1–229. Faculty of Actuaries and Institute of Actuaries. google scholar
13. De Kort, J., & Vellekoop, M. H. (2017). Existence of optimal consumption strategies in markets with longevity risk. Insurance: Mathematics and Economics, 72, 107-121. google scholar
14. Deelstra, G., Grasselli, M., & Koehl, P. F. (2003). Optimal investment strategies in the presence of a minimum guarantee. Insurance: Mathematics and Economics, 33(1), 189-207. google scholar
15. Deelstra, G., Grasselli, M., & Koehl, P. F. (2004). Optimal design of the guarantee for defined contribution funds. Journal of Economic Dynamics and Control, 28(11), 2239-2260. google scholar
16. Delong, Ł., Gerrard, R., & Haberman, S. (2008). Mean–variance optimization problems for an accumulation phase in a defined benefit plan. Insurance: Mathematics and Economics, 42(1), 107-118. google scholar
17. Di Giacinto, M., Federico, S., & Gozzi, F. (2011). Pension funds with a minimum guarantee: a stochastic control approach. Finance and Stochastics, 15(2), 297-342. google scholar
18. Di Giacinto, M., Federico, S., Gozzi, F., & Vigna, E. (2014). Income drawdown option with minimum guarantee. European Journal of Operational Research, 234(3), 610-624. google scholar
19. Donnelly, C. (2014). Quantifying mortality risk in small defined-benefit pension schemes. Scandinavian Actuarial Journal, 2014(1), 41-57. google scholar
20. Emms, P. (2012). Lifetime investment and consumption using a defined-contribution pension scheme. Journal of Economic Dynamics and Control, 36(9), 1303-1321. google scholar
21. Gomes, F. J. (2005). Portfolio choice and trading volume with loss‐averse investors. The Journal of Business, 78(2), 675-706. google scholar
22. Guan, G., & Liang, Z. (2014). Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insurance: Mathematics and Economics, 57, 58-66. google scholar
23. Guan, G., & Liang, Z. (2015). Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns. Insurance: Mathematics and Economics, 61, 99-109. google scholar
24. Haberman, S., & Vigna, E. (2002). Optimal investment strategies and risk measures in defined contribution pension schemes. Insurance: Mathematics and Economics, 31(1), 35-69. google scholar
25. Hainaut, D., & Deelstra, G. (2011). Optimal funding of defined benefit pension plans. Journal of Pension Economics and Finance, 10(1), 31-52. google scholar
26. Harlow, W. V., & Brown, K. C. (2016). Market risk, mortality risk, and sustainable retirement asset allocation: A downside risk perspective. Journal of Investment Management, 14(2), 5-32. google scholar
27. Huang, H., & Milevsky, M. A. (2016). Longevity risk and retirement income tax efficiency: A location spending rate puzzle. Insurance: Mathematics and Economics, 71, 50-62. google scholar
28. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 363-391. google scholar
29. Kırkağaç, M., & Gençtürk, Y. (2016). Bireysel emeklilik planlarında hedef fon büyüklüğüne ulaşmak için değişken katkı ve optimal yatırım stratejisi. İstatistikçiler Dergisi: İstatistik & Aktüerya, 9(2), 54-65. google scholar
30. Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. The Review Of Economics And Statistics, 247-257. google scholar
31. Merton, R. C. (1975). Optimum consumption and portfolio rules in a continuous-time model. In Stochastic Optimization Models in Finance, 621-661. google scholar
32. Owadally, I., Haberman, S., & Gómez Hernández, D. (2013). A savings plan with targeted contributions. Journal of Risk and Insurance, 80(4), 975-1000. google scholar
33. Rabin, M., & Thaler, R. H. (2001). Anomalies: Risk aversion. The Journal of Economic Perspectives, 15(1), 219-232. google scholar
34. Samuelson, P. A. (1975). Lifetime portfolio selection by dynamic stochastic programming. Stochastic Optimization Models in Finance, 517-524. google scholar
35. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323. google scholar
36. Vigna, E., & Haberman, S. (2001). Optimal investment strategy for defined contribution pension schemes. Insurance: Mathematics and Economics, 28(2), 233-262. google scholar
37. Yang, S. S., & Huang, H. C. (2009). The impact of longevity risk on the optimal contribution rate and asset allocation for defined contribution pension plans. The Geneva Papers on Risk and Insurance Issues and Practice, 34(4), 660-681. google scholar
38. Yao, H., Lai, Y., Ma, Q., & Jian, M. (2014). Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework. Insurance: Mathematics and Economics, 54, 84-92. google scholar
39. Yao, H., Chen, P., & Li, X. (2016). Multi-period defined contribution pension funds investment management with regime-switching and mortality risk. Insurance: Mathematics and Economics, 71, 103-113. google scholar