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Portfolio Optimization over a Finite Horizon with Fixed and Proportional Transaction Costs and Liquidity Constraints

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  • Stefano Baccarin

    ()
    (Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy)

  • Daniele Marazzina

    ()
    (Department of Mathematics, Polytechnic University of Milano, Italy)

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    Abstract

    We investigate a portfolio optimization problem for an agent who invests in two assets, a risk-free and a risky asset modeled by a geometric Brownian motion. The investor faces both fixed and proportional transaction costs and liquidity constraints. His objective is to maximize the expected utility from the portfolio liquidation at a terminal finite horizon. The model is formulated as a parabolic impulse control problem and we characterize the value function as the unique constrained viscosity solution of the associated quasi-variational inequality. We compute numerically the optimal policy by a an iterative finite element discretization technique, presenting extended numerical results in the case of a constant relative risk aversion utility function. Our results show that, even with small transaction costs and distant horizons, the optimal strategy is essentially a buy-and-hold trading strategy where the agent recalibrates his portfolio very few times. This contrasts sharply with the continuous interventions of the Merton's model without transaction costs.

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    File URL: http://eco83.econ.unito.it/RePEc/wp/m17.pdf
    File Function: First version, 2013
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    Bibliographic Info

    Paper provided by Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino in its series Working papers with number 017.

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    Length: 35 pages
    Date of creation: Jan 2013
    Date of revision:
    Handle: RePEc:tur:wpapnw:017

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    Keywords: Portfolio Optimization; Quasi-variational Inequalities; Transaction Costs; Viscosity Solutions;

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    1. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
    2. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    3. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    4. Kumar Muthuraman & Sunil Kumar, 2006. "Multidimensional Portfolio Optimization With Proportional Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 301-335.
    5. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    6. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
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