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Multivariate utility maximization with proportional transaction costs

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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 this 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.

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Authors and Affiliations

  1. CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Luciano Campi

  2. Department of Actuarial Mathematics and Statistics, and Maxwell Institute for Mathematical Sciences, Colin Maclaurin Building, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK

    Mark P. Owen

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  1. Luciano Campi
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  2. Mark P. Owen
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Correspondence to Luciano Campi.

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Campi, L., Owen, M.P. Multivariate utility maximization with proportional transaction costs. Finance Stoch 15, 461–499 (2011). https://doi.org/10.1007/s00780-010-0125-9

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  • DOI: https://doi.org/10.1007/s00780-010-0125-9

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