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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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    1. 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.
    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. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    4. 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.
    5. (**), 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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