基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

doi:10.15960/j.cnki.issn.1007-6093.2019.02.004

Abstract

Abstract: In this paper, we consider the optimal asset allocation problem for the defined contribution pension plan on the phase of accumulation before retirement. We assume that the pension fund can be invested into a financial market consisting of a risk-free asset and a risky asset who's price process satisfies Stein-Stein stochastic volatility model. By using the method of stochastic optimal control, we obtain the optimal investment strategy of the pension fund without or with dynamic value at risk constraint aiming to maximize the expected utility of relative wealth at retirement time, and derive the corresponding analytic expression of the optimal value function. Finally, a numerical example is provided to verify the related theoretical results and the sensitivity of the optimal investment strategy on some parameters is analyzed.

Key words: DC pension fund, Stein-Stein volatility, Hamilton-Jacobi-Bellman equation, VaR constraint

CLC Number:

F830.59
F224

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.

References 28

[1]	Devolder P, Bosch Princep M, Dominguez Fabian I. Stochastic optimal control of annuity contracts[J]. Insurance:Mathematics and Economics, 2003, 33(2):227-238.
[2]	Battocchio P, Menoncin F. Optimal pension management in a stochastic framework[J]. Insurance:Mathematics and Economics, 2004, 34(1):79-95.
[3]	Cairns A J G, Blake D, Dowd K. Stochastic lifestyling:optimal dynamic asset allocation for defined-contribution pension plans[J]. Journal of Economic Dynamics and Control, 2006, 30(5):843-877.
[4]	Gao J W. Stochastic optimal control of DC pension funds[J]. Insurance:Mathematics and Economics, 2008, 42(3):1159-1164.
[5]	Han N W, Hung M W. Optimal asset allocation for DC pension plans under inflation[J]. Insurance:Mathematics and Economics, 2012, 51(1):172-181.
[6]	常浩, 王春峰, 房振明. 通胀风险下基于HARA效用的DC型养老金计划[J]. 运筹学学报}, 2016, 20(04):39-51.
[7]	王力平, 张元萍. 考虑死亡率的DC型养老金资产配置研究的统一框架[J]. 保险研究}, 2014, 35(4):121-127.
[8]	Vigna E, Haberman S. Optimal investment strategy for defined contribution pension schemes[J]. Insurance:Mathematics and Economics, 2001, 28:233-262.
[9]	Haberman S, Vigna E. Optimal investment strategies and risk measures in defined contribution pension schemes[J]. Insurance:Mathematics and Economics, 2002, 31(1):35-69.
[10]	He L, Liang Z X. Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase[J]. Insurance:Mathematics and Economics, 2013, 52(2):404-410.
[11]	Højgaard B, Vigna E. Mean variance portfolio selection and efficient frontier for defined contribution pension schemes[R]. Aalborg:Aalborg University, 2007.
[12]	Yao H X, Yang Z, Chen P. Markowitz's mean-variance defined contribution pension fund management under inflation:A continuous-time model[J]. Insurance:Mathematics and Economics, 2013, 53(3):851-863.
[13]	Guan G H, Liang Z X. Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns[J]. Insurance:Mathematics and Economics, 2015, 61:99-109.
[14]	Cox J C. The constant elasticity of variance option pricing model[J]. The Journal of Portfolio Management, 1996, 22:15-17.
[15]	Heston S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options[J]. Review of Financial Studies, 1993, 6(2):327-343.
[16]	Stein E M, Stein J C. Stock price distributions with stochastic volatility:an analytic approach[J]. Review of Financial Studies, 1991, 4(4):727-752.
[17]	Xiao J W, Hong Z, Qin C L. The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts[J]. Insurance:Mathematics and Economics, 2007, 40(2):302-310.
[18]	Gao J W. Optimal portfolios for DC pension plans under a CEV model[J]. Insurance:Mathematics and Economics, 2009, 44(3):479-490.
[19]	张初兵, 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.
[20]	Sun J Y, Li Z F, Li Y W. Equilibrium investment strategy for DC pension plan with inflation and stochastic income under Heston's SV model[J]. Mathematical Problems in Engineering, 2016, 2016(3):1-18.
[21]	Yiu K F C. Optimal portfolios under a value-at-risk constraint[J]. Journal of Economic Dynamics and Control, 2004, 28:1317-1334.
[22]	Alexander G J, Baptista A M. A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model[J]. Management Science, 2004, 50(9):1261-1273.
[23]	Cuoco D, He H, Issaenko S. Optimal dynamic trading strategies with risk limits[J]. Operational Research, 2008, 56(2):358-368
[24]	Chen S M, Li Z F, Li K M. Optimal investment-reinsurance policy for an insurance company with VaR constraint[J]. Insurance:Mathematics and Economics, 2010, 47:144-153.
[25]	Zhang N, Jin Z, Li S, et al. Optimal reinsurance under dynamic VaR constraint[J]. Insurance:Mathematics and Economics, 2016, 71:232-243.
[26]	Zhang Q Y, Gao Y. Portfolio selection based on a benchmark process with dynamic value-at-risk constraints[J]. Journal of Computational and Applied Mathematics, 2017, 313:440-447.
[27]	伊博, 李仲飞, 曾燕. 基于动态VaR约束与随机波动率模型的最优投资策略[J]. 运筹学学报}, 2012, 16(2):77-90.
[28]	Pirvu T A. Portfolio optimization under the Value-at-Risk constraint[J]. Quantitative Finance, 2007, 7:125-136.

Optimal investment strategy for the DC pension fund with Stein-Stein volatility and dynamic VaR constraint

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