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A set optimization approach to utility maximization under transaction costs

Author

Listed:
  • Andreas H. Hamel

    (Free University Bozen)

  • Sophie Qingzhen Wang

    (Harvard University)

Abstract

A set optimization approach to multi-utility maximization is presented, and duality results are obtained for discrete market models with proportional transaction costs. The novel approach allows us to obtain results for non-complete preferences, where the formulas derived closely resemble but generalize the scalar case.

Suggested Citation

  • Andreas H. Hamel & Sophie Qingzhen Wang, 2017. "A set optimization approach to utility maximization under transaction costs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 257-275, November.
    • Handle: RePEc:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0195-7
    DOI: 10.1007/s10203-017-0195-7
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    References listed on IDEAS

    as
    1. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    2. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    3. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, vol. 15(3), pages 461-499, September.
    4. repec:dau:papers:123456789/5980 is not listed on IDEAS
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    6. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    7. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
    8. repec:dau:papers:123456789/2318 is not listed on IDEAS
    9. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
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    Citations

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    Cited by:

    1. Andreas H Hamel & Birgit Rudloff & Zhou Zhou, 2019. "Robust no arbitrage and the solvability of vector-valued utility maximization problems," Papers 1909.00354, arXiv.org.
    2. Birgit Rudloff & Firdevs Ulus, 2019. "Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization," Papers 1904.09456, arXiv.org, revised Oct 2020.
    3. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.

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    More about this item

    Keywords

    Utility maximization; Non-complete preference; Multi-utility representation; Set optimization; Duality theory; Transaction costs;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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