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Multi-stage portfolio selection problem with dynamic stochastic dominance constraints

Author

Listed:
  • Yu Mei

    (Xi’an Jiaotong University
    Xi’an International Academy for Mathematics and Mathematical Technology)

  • Zhiping Chen

    (Xi’an Jiaotong University
    Xi’an International Academy for Mathematics and Mathematical Technology)

  • Jia Liu

    (Xi’an Jiaotong University
    Xi’an International Academy for Mathematics and Mathematical Technology)

  • Bingbing Ji

    (Xi’an Jiaotong University
    Xi’an International Academy for Mathematics and Mathematical Technology)

Abstract

We study the multi-stage portfolio selection problem where the utility function of an investor is ambiguous. The ambiguity is characterized by dynamic stochastic dominance constraints, which are able to capture the dynamics of the random return sequence during the investment process. We propose a multi-stage dynamic stochastic dominance constrained portfolio selection model, and use a mixed normal distribution with time-varying weights and the K-means clustering technique to generate a scenario tree for the transformation of the proposed model. Based on the scenario tree representation, we derive two linear programming approximation problems, using the sampling approach or the duality theory, which provide an upper bound approximation and a lower bound approximation for the original nonconvex problem. The upper bound is asymptotically tight with infinitely many samples. Numerical results illustrate the practicality and efficiency of the proposed new model and solution techniques.

Suggested Citation

  • Yu Mei & Zhiping Chen & Jia Liu & Bingbing Ji, 2022. "Multi-stage portfolio selection problem with dynamic stochastic dominance constraints," Journal of Global Optimization, Springer, vol. 83(3), pages 585-613, July.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:3:d:10.1007_s10898-021-01113-z
    DOI: 10.1007/s10898-021-01113-z
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    1. Nilay Noyan & Gábor Rudolf, 2013. "Optimization with Multivariate Conditional Value-at-Risk Constraints," Operations Research, INFORMS, vol. 61(4), pages 990-1013, August.
    2. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    3. Andrea Consiglio & Angelo Carollo & Stavros A. Zenios, 2016. "A parsimonious model for generating arbitrage-free scenario trees," Quantitative Finance, Taylor & Francis Journals, vol. 16(2), pages 201-212, February.
    4. Giorgio Consigli & Vittorio Moriggia & Sebastiano Vitali, 2020. "Long-term individual financial planning under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 292(2), pages 973-1000, September.
    5. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    6. Miloš Kopa & Vittorio Moriggia & Sebastiano Vitali, 2018. "Individual optimal pension allocation under stochastic dominance constraints," Annals of Operations Research, Springer, vol. 260(1), pages 255-291, January.
    7. 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.
    8. Georg Pflug & Alois Pichler, 2015. "Dynamic generation of scenario trees," Computational Optimization and Applications, Springer, vol. 62(3), pages 641-668, December.
    9. Zhiping Chen & Giorgio Consigli & Jia Liu & Gang Li & Tianwen Fu & Qianhui Hu, 2017. "Multi-Period Risk Measures and Optimal Investment Policies," International Series in Operations Research & Management Science, in: Giorgio Consigli & Daniel Kuhn & Paolo Brandimarte (ed.), Optimal Financial Decision Making under Uncertainty, chapter 0, pages 1-34, Springer.
    10. Michael A.H. Dempster & Elena A. Medova & Yee Sook Yong, 2011. "Comparison of Sampling Methods for Dynamic Stochastic Programming," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 389-425, Springer.
    11. James Ming Chen, 2017. "Risk and Uncertainty," Quantitative Perspectives on Behavioral Economics and Finance, in: Econophysics and Capital Asset Pricing, chapter 0, pages 189-211, Palgrave Macmillan.
    12. Dupačová, Jitka & Kopa, Miloš, 2014. "Robustness of optimal portfolios under risk and stochastic dominance constraints," European Journal of Operational Research, Elsevier, vol. 234(2), pages 434-441.
    13. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
    14. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    15. Xi Yang & Jacek Gondzio & Andreas Grothey, 2010. "Asset liability management modelling with risk control by stochastic dominance," Journal of Asset Management, Palgrave Macmillan, vol. 11(2), pages 73-93, June.
    16. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "A dynamic stochastic programming model for international portfolio management," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1501-1524, March.
    17. Michal Kaut & Stein Wallace, 2011. "Shape-based scenario generation using copulas," Computational Management Science, Springer, vol. 8(1), pages 181-199, April.
    18. Benjamin Armbruster & James Luedtke, 2015. "Models and formulations for multivariate dominance-constrained stochastic programs," IISE Transactions, Taylor & Francis Journals, vol. 47(1), pages 1-14, January.
    19. Meskarian, Rudabeh & Xu, Huifu & Fliege, Jörg, 2012. "Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 216(2), pages 376-385.
    20. Moriggia, Vittorio & Kopa, Miloš & Vitali, Sebastiano, 2019. "Pension fund management with hedging derivatives, stochastic dominance and nodal contamination," Omega, Elsevier, vol. 87(C), pages 127-141.
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