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On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility

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  • Černý, Aleš
  • Maccheroni, Fabio
  • Marinacci, Massimo
  • Rustichini, Aldo

Abstract

We report a surprising link between optimal portfolios generated by a special type of variational preferences called divergence preferences (see Maccheroni et al., 2006) and optimal portfolios generated by classical expected utility. As a special case, we connect optimization of truncated quadratic utility (see Černý, 2003) to the optimal monotone mean–variance portfolios (see Maccheroni et al., 2009), thus simplifying the computation of the latter.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:386-395
    DOI: 10.1016/j.jmateco.2012.08.006
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    References listed on IDEAS

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    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Cern›, Ales, 2002. "Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets," Royal Economic Society Annual Conference 2002 41, Royal Economic Society.
    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. Aleš Černý & Jan Kallsen, 2008. "Mean–Variance Hedging And Optimal Investment In Heston'S Model With Correlation," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 473-492, July.
    5. 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.
    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. 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.
    8. Hanqing Jin & Harry Markowitz & Xun Yu Zhou, 2006. "A Note On Semivariance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 53-61, January.
    9. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. 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.
    2. Alev{s} v{C}ern'y, 2019. "Semimartingale theory of monotone mean--variance portfolio allocation," Papers 1903.06912, arXiv.org, revised Jan 2020.
    3. Samuel Drapeau & Michael Kupper & Antonis Papapantoleon, 2012. "A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents," Papers 1212.6732, arXiv.org, revised Dec 2013.
    4. Eric André, 2014. "Crisp Fair Gambles," Working Papers halshs-00984352, HAL.
    5. Yang Shen & Bin Zou, 2022. "Cone-constrained Monotone Mean-Variance Portfolio Selection Under Diffusion Models," Papers 2205.15905, arXiv.org.

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    More about this item

    Keywords

    Optimal portfolio; Truncated quadratic utility; Monotone mean–variance preferences; Divergence preferences; HARA utility; Monotone hull; Translation-invariant hull;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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