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Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

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  • Guan, Guohui
  • Liang, Zongxia

Abstract

This paper studies the risk management in a defined contribution (DC)pension plan. The financial market consists of cash, bond and stock. The interest rate in our model is assumed to follow an Ornstein–Uhlenbeck process while the contribution rate follows a geometric Brownian Motion. Thus, the pension manager has to hedge the risks of interest rate, stock and contribution rate. Different from most works in DC pension plan, the pension manger has to obtain the optimal allocations under loss aversion and Value-at-Risk(VaR) constraints. The loss aversion pension manager is sensitive to losses while the VaR pension manager has to ensure the quality of wealth at retirement. Since these problems are not standard concave optimization problems, martingale method is applied to derive the optimal investment strategies. Explicit solutions are obtained under these two optimization criterions. Moreover, sensitivity analysis is presented in the end to show the economic behaviors under these two criterions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:69:y:2016:i:c:p:224-237
    DOI: 10.1016/j.insmatheco.2016.05.014
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    Cited by:

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    2. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    3. Xiao Xu, 2020. "The optimal investment strategy of a DC pension plan under deposit loan spread and the O-U process," Papers 2005.10661, arXiv.org.
    4. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    5. John Armstrong & Damiano Brigo & Alex S. L. Tse, 2020. "The importance of dynamic risk constraints for limited liability operators," Papers 2011.03314, arXiv.org.
    6. Liudmila Reshetnikova & Natalia Boldyreva & Maria Perevalova & Svetlana Kalayda & Zhanna Pisarenko, 2021. "Conditions for the Growth of the “Silver Economy” in the Context of Sustainable Development Goals: Peculiarities of Russia," JRFM, MDPI, vol. 14(9), pages 1-18, August.
    7. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    8. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    9. Guohui Guan & Zongxia Liang & Yi Xia, 2023. "Optimal management of DB pension fund under both underfunded and overfunded cases," Papers 2302.08731, arXiv.org.
    10. Pengyu Wei & Charles Yang, 2023. "Optimal investment for defined-contribution pension plans under money illusion," Review of Quantitative Finance and Accounting, Springer, vol. 61(2), pages 729-753, August.
    11. Qin Yang & Jinfeng Liu & Xing Liu & Cejun Cao & Wei Zhang, 2019. "A Two-Sided Matching Model for Task Distribution in Ridesharing: A Sustainable Operations Perspective," Sustainability, MDPI, vol. 11(7), pages 1-16, April.
    12. Chen, Zheng & Li, Zhongfei & Zeng, Yan & Sun, Jingyun, 2017. "Asset allocation under loss aversion and minimum performance constraint in a DC pension plan with inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 137-150.
    13. Guohui Guan & Zongxia Liang & Yi xia, 2021. "Optimal management of DC pension fund under relative performance ratio and VaR constraint," Papers 2103.04352, arXiv.org.
    14. Anne MacKay & Adriana Ocejo, 2022. "Portfolio Optimization With a Guaranteed Minimum Maturity Benefit and Risk-Adjusted Fees," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1021-1049, June.
    15. Chen, Zheng & Li, Zhongfei & Zeng, Yan, 2023. "Portfolio choice with illiquid asset for a loss-averse pension fund investor," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 60-83.
    16. Wang, Suxin & Rong, Ximin & Zhao, Hui, 2019. "Optimal investment and benefit payment strategy under loss aversion for target benefit pension plans," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 205-218.

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    More about this item

    Keywords

    IE12; IE13; IE43; IB81; Defined contribution pension plan; Portfolio choice; Stochastic interest rate; Stochastic contribution rate; Loss aversion; Value-at-Risk; Martingale method;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles

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