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Minimal Quantile Functions Subject to Stochastic Dominance Constraints

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  • 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.

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  • 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
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    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.
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