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Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs

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  • Colin Atkinson
  • Emmeline Storey

Abstract

Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs.

Suggested Citation

  • Colin Atkinson & Emmeline Storey, 2010. "Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 323-357.
    • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:4:p:323-357
    DOI: 10.1080/13504860903336437
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    References listed on IDEAS

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    1. C. Atkinson & S. Mokkhavesa, 2004. "Multi-asset portfolio optimization with transaction cost," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(2), pages 95-123.
    2. Jörn Sass, 2005. "Portfolio optimization under transaction costs in the CRR model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 239-259, June.
    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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