IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2008.02420.html
   My bibliography  Save this paper

Minimal Quantile Functions Subject to Stochastic Dominance Constraints

Author

Listed:
  • Xiangyu Wang
  • Jianming Xia
  • Zuo Quan Xu
  • Zhou Yang

Abstract

We consider a problem of finding an SSD (second-order stochastic dominance)-minimal quantile function subject to the mixture of FSD (first-order stochastic dominance) and SSD constraints. The SSD-minimal solution is explicitly worked out and has a close relation to the Skorokhod problem. This result is then applied to explicitly solve a risk minimizing problem in financial economics.

Suggested Citation

  • Xiangyu Wang & Jianming Xia & Zuo Quan Xu & Zhou Yang, 2020. "Minimal Quantile Functions Subject to Stochastic Dominance Constraints," Papers 2008.02420, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2008.02420
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2008.02420
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jianming Xia & Xun Yu Zhou, 2016. "Arrow–Debreu Equilibria For Rank-Dependent Utilities," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 558-588, July.
    2. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    3. repec:dau:papers:123456789/5392 is not listed on IDEAS
    4. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    5. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    6. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximization with intractable claims," Papers 2304.06938, arXiv.org, revised Jul 2023.
    2. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    3. Pengyu Wei & Zuo Quan Xu, 2021. "Dynamic growth-optimum portfolio choice under risk control," Papers 2112.14451, arXiv.org.
    4. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    5. Jianming Xia, 2023. "Benchmark Beating with the Increasing Convex Order," Papers 2311.01692, arXiv.org.
    6. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    7. Jing Peng & Pengyu Wei & Zuo Quan Xu, 2022. "Relative growth rate optimization under behavioral criterion," Papers 2211.05402, arXiv.org.
    8. Zuo Quan Xu, 2021. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Papers 2108.06940, arXiv.org, revised Aug 2022.
    9. 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.
    10. 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.
    11. Zuo Quan Xu, 2014. "A Note on the Quantile Formulation," Papers 1403.7269, arXiv.org, revised Apr 2014.
    12. Xue Dong He & Hanqing Jin & Xun Yu Zhou, 2015. "Dynamic Portfolio Choice When Risk Is Measured by Weighted VaR," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 773-796, March.
    13. Mingyu Xu & Zuo Quan Xu & Xun Yu Zhou, 2022. "$g$-Expectation of Distributions," Papers 2208.06535, arXiv.org.
    14. Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
    15. Rose‐Anne Dana, 2005. "A Representation Result For Concave Schur Concave Functions," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 613-634, October.
    16. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    17. Bahman Angoshtari & Shida Duan, 2024. "Rank-Dependent Predictable Forward Performance Processes," Papers 2403.16228, arXiv.org.
    18. van Bilsen, Servaas & Laeven, Roger J.A., 2020. "Dynamic consumption and portfolio choice under prospect theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 224-237.
    19. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, March.
    20. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2008.02420. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.