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Optimal management and inflation protection for defined contribution pension plans

Author

Listed:
  • Zhang, Aihua
  • Korn, Ralf
  • Ewald, Christian-Oliver

Abstract

Due to the increasing risk of inflation and diminishing pension benefits, insurance companies have started selling in°ation-linked products. Selling such products the insurance company takes over some or all of the inflation risk from their customers. On the other side financial derivatives which are linked to inflation such as inflation linked bonds are traded on financial markets and appear to be of increasing popularity. The insurance company can use these products to hedge its own inflation risk. In this article we study how to optimally manage a pension fund taking positions in a money market account, a stock and an inflation linked bond, while financing investments through a continuous stochastic income stream such as the plan member's contributions. We use the martingale method in order to compute an analytic expression for the optimal strategy and express it in terms of observable market variables.

Suggested Citation

  • Zhang, Aihua & Korn, Ralf & Ewald, Christian-Oliver, 2007. "Optimal management and inflation protection for defined contribution pension plans," MPRA Paper 3300, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3300
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    References listed on IDEAS

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    1. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    2. Paolo BATTOCCHIO & Francesco MENONCIN, 2002. "Optimal Pension Management under Stochastic Interest Rates, Wages, and Inflation," LIDAM Discussion Papers IRES 2002021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 19-55, May.
    4. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    5. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    2. 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.
    3. Xiaoyi Zhang, 2022. "Optimal DC Pension Management Under Inflation Risk With Jump Diffusion Price Index and Cost of Living Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1253-1270, June.
    4. Gao, Shuping & Guo, Junyi & Liang, Xiaoqing, 2025. "Bayesian adaptive portfolio optimization for DC pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 262-274.
    5. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    6. Zhang, Jiannan & Chen, Ping & Jin, Zhuo & Li, Shuanming, 2025. "Optimal strategies for collective defined contribution plans when the stock and labor markets are co-integrated," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    7. Mirco Mahlstedt & Rudi Zagst, 2016. "Inflation Protected Investment Strategies," Risks, MDPI, vol. 4(2), pages 1-21, March.
    8. Wu, Huiling & Zeng, Yan, 2015. "Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 396-408.
    9. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
    10. Fulli-Lemaire, Nicolas, 2013. "Alternative inflation hedging strategies for ALM," MPRA Paper 43755, University Library of Munich, Germany.
    11. Fulli-Lemaire, Nicolas, 2012. "Alternative Inflation Hedging Portfolio Strategies: Going Forward Under Immoderate Macroeconomics," MPRA Paper 42854, University Library of Munich, Germany.
    12. 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.
    13. Jian Pan & Qingxian Xiao, 2017. "Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 491-519, June.
    14. Aihua Zhang & Christian-Oliver Ewald, 2010. "Optimal investment for a pension fund under inflation risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 353-369, April.
    15. Wu, Huiling & Zhang, Ling & Chen, Hua, 2015. "Nash equilibrium strategies for a defined contribution pension management," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 202-214.
    16. 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.
    17. Xiaoyi Zhang & Junyi Guo, 2018. "The Role of Inflation-Indexed Bond in Optimal Management of Defined Contribution Pension Plan During the Decumulation Phase," Risks, MDPI, vol. 6(2), pages 1-16, March.
    18. 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.
    19. 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.
    20. 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.
    21. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    22. Li, Danping & Rong, Ximin & Zhao, Hui, 2015. "Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 28-44.
    23. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    24. Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.

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    More about this item

    Keywords

    Pension mathematics; in°ation; long-term investment; stochastic optimal control; martingale method;
    All these keywords.

    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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