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Multivariate utility maximization with proportional transaction costs

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  • Luciano Campi
  • Mark P. Owen

Abstract

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor's preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given terminal date. We prove the existence of an optimal portfolio process under the assumption of asymptotic satiability of the value function. Sufficient conditions for asymptotic satiability of the value function include reasonable asymptotic elasticity of the utility function, or a growth condition on its dual function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer.

Suggested Citation

  • Luciano Campi & Mark P. Owen, 2008. "Multivariate utility maximization with proportional transaction costs," Papers 0811.3889, arXiv.org, revised Apr 2009.
    • Handle: RePEc:arx:papers:0811.3889
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    References listed on IDEAS

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    1. Yuri M. Kabanov & Günter Last, 2002. "Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 63-70, January.
    2. 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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