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Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model

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  • Gao, Jianwei
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    Abstract

    This paper focuses on the constant elasticity of variance (CEV) model for studying the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using Legendre transform, dual theory and variable change technique, we derive the explicit solutions for the power and exponential utility functions in two different periods (before and after retirement). Each solution contains a modified factor which reflects an investor's decision to hedge the volatility risk. In order to investigate the influence of the modified factor on the optimal strategy, we analyze the property of the modified factor. The results show that the dynamic behavior of the modified factor for the power utility mainly depends on the time and the investor's risk aversion coefficient, whereas it only depends on the time in the exponential case.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(09)00013-4
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 1 (August)
    Pages: 9-18

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:9-18
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

    Keywords: Annuity Defined contribution pension plan Stochastic optimal control Legendre transform CEV model;

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    15. Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
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    Cited by:

    1. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    2. Chang, Hao & Chang, Kai, 2017. "Optimal consumption–investment strategy under the Vasicek model: HARA utility and Legendre transform," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 215-227.
    3. Jung, Eun Ju & Kim, Jai Heui, 2012. "Optimal investment strategies for the HARA utility under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 667-673.
    4. Guan, Guohui & Liang, Zongxia, 2016. "Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 224-237.
    5. Zhang, Miao & Chen, Ping, 2016. "Mean–variance asset–liability management under constant elasticity of variance process," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 11-18.
    6. Guan, Guohui & Liang, Zongxia, 2016. "A stochastic Nash equilibrium portfolio game between two DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 237-244.
    7. Gao, Jianwei, 2010. "An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 511-530, June.
    8. Li, Danping & Rong, Ximin & Zhao, Hui & Yi, Bo, 2017. "Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 6-20.

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