基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

doi:10.15960/j.cnki.issn.1007-6093.2023.01.005

Abstract

Abstract:

From the dual perspective of the DC pension plan members and the manager, we investigate the asset allocation of a DC pension plan under a VaR-PI constraint by maximizing a weighted utility of the two parties. Assuming that the DC pension plan members and the manager are loss averse and we use two S-shaped utility functions to demonstrate the loss aversion behavior. The VaR constraint and a weighed utility lead to a complex, nonconcave utility maximization problem. We apply the Lagrange duality theory and the concavification technique to derive the optimal wealth and the optimal portfolio processes. Numerical results show that the manager shall take a much riskier portfolio strategy when the benefits of the DC pension plan members are paid much more attention. The VaR constraint can improve the risk management of the DC pension plan.

Key words: VaR constraint, DC pension plan, loss aversion, weighted utility

CLC Number:

Yinghui DONG, Siyuan WEI, Zihan YIN. Optimal investment of DC pension plan under a weighted utility and VaR-PI constraint[J]. Operations Research Transactions, 2023, 27(1): 70-86.

Figures/Tables 13

References 16

1	Boulier J F , Huang S J , Taillard G . Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund[J]. Insurance Mathematics and Economics, 2001, 28, 173- 189. doi: 10.1016/S0167-6687(00)00073-1
2	张妨兵, 荣喜民. 均值-方差模型下DC型养老金的随机最优控制[J]. 系统工程理论与实践, 2012, 32 (6): 1314- 1323.
3	何林. DC型企业年金最优资产配置和给付方案问题研究[J]. 中国管理科学, 2015, 23 (8): 39- 45.
4	孙景云, 李仲飞, 李永武. 动态投资目标下DC型养老基金的最优投资策略[J]. 系统工程理论与实践, 2017, 37 (9): 2209- 2221.
5	Dong Y H , Zheng H . Optimal investment of DC pension plan under short-selling constraints and portfolio insurance[J]. Insurance: Mathematics and Economics, 2019, 85, 47- 59. doi: 10.1016/j.insmatheco.2018.12.005
6	Chen Z , Li Z F , Zeng Y , et al. Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk[J]. Insurance Mathematics and Economics, 2017, 75, 137- 150. doi: 10.1016/j.insmatheco.2017.05.009
7	Guan G H , Liang Z X . Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints[J]. Insurance: Mathematics and Economics, 2016, 69, 224- 237. doi: 10.1016/j.insmatheco.2016.05.014
8	Kahneman D , Tversky A . Prospect theory: an analysis of decision under risk[J]. Econometrica, 1979, 47, 263- 292. doi: 10.2307/1914185
9	Tversky A , Kahneman D . Advances in prospect theory: cumulative representation of uncertainty[J]. Journal of Risk and Uncertainty, 1992, 5, 297- 323. doi: 10.1007/BF00122574
10	Dong Y H , Zheng H . Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan[J]. European Journal of Operation Research, 2020, 281, 341- 356.
11	王传玉, 付春艳, 盛国祥. 基于通货膨胀和最低保障的DC养老金最优投资[J]. 运筹与管理, 2018, 27 (2): 193- 199.
12	蔡晶晶, 董迎辉, 吕文欣, 等. VaR约束下带最低保障的DC型养老金的最优投资[J]. 系统工程理论与实践, 2021, 41 (05): 1252- 1262.
13	He L , Liang Z X , Liu Y , et al. Weighted utility optimization of the participating endowment contract[J]. Scandinavian Actuarial Journal, 2020, 7, 577- 613.
14	Carpenter , Jennifer N . Does option compensation increase managerial risk appetite[J]. The Journal of Finance, 2000, 55 (5): 2311- 2331.
15	He L , Liang Z X , Liu Y , et al. Optimal control of DC pension plan management under two incentive schemes[J]. North American Actuarial Journal, 2019, 23 (1): 120- 141.
16	Reichlin C . Utility maximization with a given pricing measure when the utility is not necessarily concave[J]. Mathematics and Financial Economics, 2013, 7 (4): 531- 556.

$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ \pi^{, \beta^}(0)(a=0.5) $	14.55	11.69	8.35	10.04	11.64
$ \pi^{, \beta^}(0)(a=1) $	17.57	15.58	12.93	14.33	15.52
$ \pi^{, \beta^, 0.05}(a=0.5) $	12.94	10.41	8.32	9.29	10.42
$ \pi^{, \beta^, 0.05}(a=1) $	16.83	14.59	12.46	13.30	14.26

$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ E(X^{\pi^, \beta^}(T)) $	108.6	105.03	101.84	103.17	104.81
$ \sigma(X^{\pi^, \beta^}(T)) $	39.86	33.63	29.30	30.80	33.28
$ P(X^{\pi^, \beta^}(T)=L) $	0.14	0.10	0.06	0.08	0.1
$ P(X^{\pi^, \beta^}(T)>L) $	0.85	0.90	0.94	0.92	0.9

$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ E(X^{\pi^, \beta^, 0.05}(T)) $	102.85	99.62	97.62	99.24	99.73
$ \sigma(X^{\pi^, \beta^, 0.0.05}(T)) $	28.06	22.90	21.76	23.15	23.59
$ P(X^{\pi^{, \beta^, 0.05}}(T)=L) $	0.05	0.05	0.05	0.05	0.05
$ P(X^{\pi^{, \beta^, 0.05}}(T)>L) $	0.95	0.95	0.95	0.95	0.95

[1]	SUN Jingyun, TIAN Lina, CHEN Zheng. Optimal investment strategy for the DC pension fund with Stein-Stein volatility and dynamic VaR constraint [J]. Operations Research Transactions, 2019, 23(2): 44-56.
[2]	YI Bo, LI Zhong-Fei, ZENG Yan. Optimal investment strategy with stochastic volatility and dynamic VaR constraint [J]. Operations Research Transactions, 2012, 16(2): 77-90.
[3]	Mi Hui, ZHANG Shu-Guang. Continuous-time Portfolio Selection with Loss Aversion in an Incomplete Market [J]. Operations Research Transactions, 2012, 16(1): 1-12.

Optimal investment of DC pension plan under a weighted utility and VaR-PI constraint

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