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Optimal Investment Under Transaction Costs


  • Sait Tunc
  • Mehmet A. Donmez
  • Suleyman S. Kozat


We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we next solve optimal portfolio selection in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations.

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  • Sait Tunc & Mehmet A. Donmez & Suleyman S. Kozat, 2012. "Optimal Investment Under Transaction Costs," Papers 1203.4153,, revised Jul 2012.
  • Handle: RePEc:arx:papers:1203.4153

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    References listed on IDEAS

    1. Michael W. Brandt & Pedro Santa-Clara & Rossen Valkanov, 2009. "Parametric Portfolio Policies: Exploiting Characteristics in the Cross-Section of Equity Returns," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3411-3447, September.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    4. 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.
    5. Markowitz, Harry M, 1991. "Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
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    Cited by:

    1. Fotis Papailias & Dimitrios Thomakos, 2015. "Covariance averaging for improved estimation and portfolio allocation," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(1), pages 31-59, February.

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