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On the density of properly maximal claims in financial markets with transaction costs

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  • Saul Jacka
  • Abdelkarem Berkaoui

Abstract

We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure. This result fails in the presence of transaction costs. A properly maximal claim is one which does have this property. We show that the properly maximal claims are dense in the set of maximal claims (with the topology of convergence in probability).

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  • Saul Jacka & Abdelkarem Berkaoui, 2006. "On the density of properly maximal claims in financial markets with transaction costs," Papers math/0602592, arXiv.org, revised May 2007.
    • Handle: RePEc:arx:papers:math/0602592
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    References listed on IDEAS

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

    1. Erhan Bayraktar & Xiang Yu, 2015. "Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices," Papers 1504.00310, arXiv.org, revised Aug 2018.
    2. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382, arXiv.org, revised Jul 2016.

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