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Dynamic Portfolio Optimization in Discrete-Time with Transaction Costs


  • Colin Atkinson
  • Gary Quek


A discrete-time model of portfolio optimization is studied under the effects of proportional transaction costs. A general class of underlying probability distributions is assumed for the returns of the asset prices. An investor with an exponential utility function seeks to maximize the utility of terminal wealth by determining the optimal investment strategy at the start of each time step. Dynamic programming is used to derive an algorithm for computing the optimal value function and optimal boundaries of the no-transaction region at each time step. In the limit of small transaction costs, perturbation analysis is applied to obtain the optimal value function and optimal boundaries at any time step in the rebalancing of the portfolio.

Suggested Citation

  • Colin Atkinson & Gary Quek, 2012. "Dynamic Portfolio Optimization in Discrete-Time with Transaction Costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 265-298, August.
  • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:265-298 DOI: 10.1080/1350486X.2011.620775

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    References listed on IDEAS

    1. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
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    6. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
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