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Robust no arbitrage and the solvability of vector-valued utility maximization problems

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  • Andreas H Hamel
  • Birgit Rudloff
  • Zhou Zhou

Abstract

A market model with $d$ assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a num\`eraire is not assumed. It is shown that robust no arbitrage holds if, and only if, there exists a Pareto solution for some vector-valued utility maximization problem with component-wise utility functions. Moreover, it is demonstrated that a consistent price process can be constructed from the Pareto maximizer.

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  • 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.
    • Handle: RePEc:arx:papers:1909.00354
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    References listed on IDEAS

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    6. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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