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Convex duality and Orlicz spaces in expected utility maximization

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  • Sara Biagini
  • Aleš Černý

Abstract

In this paper, we report further progress toward a complete theory of state‐independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions, we establish a surprising Fenchel duality result on conjugate Orlicz spaces, offering a new economic insight into the nature of primal optima and providing a fresh perspective on the classical papers of Kramkov and Schachermayer. The analysis points to an intriguing interplay between no‐arbitrage conditions and standard convex optimization and motivates the study of the fundamental theorem of asset pricing for Orlicz tame strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:1:p:85-127
    DOI: 10.1111/mafi.12209
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    Cited by:

    1. Aleš Černý, 2020. "Semimartingale theory of monotone mean–variance portfolio allocation," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1168-1178, July.
    2. Černý, Aleš & Czichowsky, Christoph & Kallsen, Jan, 2021. "Numeraire-invariant quadratic hedging and mean–variance portfolio allocation," LSE Research Online Documents on Economics 112612, London School of Economics and Political Science, LSE Library.
    3. Alev{s} v{C}ern'y & Christoph Czichowsky & Jan Kallsen, 2021. "Numeraire-invariant quadratic hedging and mean--variance portfolio allocation," Papers 2110.09416, arXiv.org, revised Jan 2023.
    4. Alev{s} v{C}ern'y, 2020. "The Hansen ratio in mean--variance portfolio theory," Papers 2007.15980, arXiv.org.

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