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On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization

Author

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  • F. CONG

    (Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, The Netherlands)

  • C. W. OOSTERLEE

    (Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, The Netherlands†Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, The Netherlands)

Abstract

We consider robust pre-commitment and time-consistent mean-variance optimal asset allocation strategies, that are required to perform well also in a worst-case scenario regarding the development of the asset price. We show that worst-case scenarios for both strategies can be found by solving a specific equation each time step. In the unconstrained asset allocation case, the robust pre-commitment as well as the time-consistent strategy are identical to the corresponding robust myopic strategies, by which investors perform robust portfolio control only for one time step and conduct a risk-free strategy afterwards. In the experiments, the robustness of pre-commitment and time-consistent strategies is studied in detail. Our analysis and numerical results indicate that the time-consistent allocation strategy is more stable when possible incorrect assumptions regarding the future asset development are modeled and taken into account. In some situations, the time-consistent strategy can even generate higher efficient frontiers than the pre-commitment strategy (which is counter-intuitive), because the time-consistency restriction appears to protect an investor in such a situation.

Suggested Citation

  • F. Cong & C. W. Oosterlee, 2017. "On Robust Multi-Period Pre-Commitment And Time-Consistent Mean-Variance Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:07:n:s0219024917500492
    DOI: 10.1142/S0219024917500492
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    References listed on IDEAS

    as
    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    2. Wang, J. & Forsyth, P.A., 2010. "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 207-230, February.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    4. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    5. Gulpinar, Nalan & Rustem, Berc, 2007. "Worst-case robust decisions for multi-period mean-variance portfolio optimization," European Journal of Operational Research, Elsevier, vol. 183(3), pages 981-1000, December.
    6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    7. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    8. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    9. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    10. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
    11. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    12. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2014. "Recent Developments in Robust Portfolios with a Worst-Case Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 103-121, April.
    13. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    14. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    15. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
    16. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    17. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    18. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    19. Gerrard, Russell & Haberman, Steven & Vigna, Elena, 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 321-342, October.
    20. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    21. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    22. Sun, Jingyun & Li, Zhongfei & Zeng, Yan, 2016. "Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 158-172.
    23. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    24. Michael J. Best & Robert R. Grauer, 1991. "Sensitivity Analysis for Mean-Variance Portfolio Problems," Management Science, INFORMS, vol. 37(8), pages 980-989, August.
    25. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
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    Cited by:

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    3. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    4. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    5. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    6. Kristoffer Andersson & Cornelis W. Oosterlee, 2023. "D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options," Papers 2308.10556, arXiv.org, revised Sep 2023.
    7. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    8. Masashi Ieda, 2022. "Continuous-Time Portfolio Optimization for Absolute Return Funds," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(4), pages 675-696, December.

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