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Semimartingale theory of monotone mean–variance portfolio allocation

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  • Aleš Černý

Abstract

We study dynamic optimal portfolio allocation for monotone mean–variance preferences in a general semimartingale model. Armed with new results in this area, we revisit the work of Cui et al. and fully characterize the circumstances under which one can set aside a nonnegative cash flow while simultaneously improving the mean–variance efficiency of the left‐over wealth. The paper analyzes, for the first time, the monotone hull of the Sharpe ratio and highlights its relevance to the problem at hand.

Suggested Citation

  • Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:3:p:1168-1178
    DOI: 10.1111/mafi.12241
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    References listed on IDEAS

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    1. Aleš Černý, 2003. "Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets," Review of Finance, European Finance Association, vol. 7(2), pages 191-233.
    2. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    4. Sara Biagini & Aleš Černý, 2020. "Convex duality and Orlicz spaces in expected utility maximization," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 85-127, January.
    5. Černý, Aleš & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2012. "On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 386-395.
    6. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    8. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
    9. Nicole Bäuerle & Stefanie Grether, 2015. "Complete markets do not allow free cash flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 137-146, April.
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    Cited by:

    1. Yang Shen & Bin Zou, 2022. "Cone-constrained Monotone Mean-Variance Portfolio Selection Under Diffusion Models," Papers 2205.15905, arXiv.org.
    2. Alev{s} v{C}ern'y, 2020. "The Hansen ratio in mean--variance portfolio theory," Papers 2007.15980, arXiv.org.
    3. Carlo Alberto Magni & Andrea Marchioni, 2022. "Performance attribution, time-weighted rate of return, and clean finite change sensitivity index," Journal of Asset Management, Palgrave Macmillan, vol. 23(1), pages 62-72, February.

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