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Boundedness of the Value Function of the Worst-Case Portfolio Selection Problem with Linear Constraints

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  • Nikolay A Andreev

    (National Research University Higher School of Economics)

Abstract

We study the boundedness properties of the value function for a general worst-case scenario stochastic dynamic programming problem. For the portfolio selection problem,we present sufficient economically reasonable conditions for the finitness and uniform boundedness of the value function. The results can be used to decide if the problem is ill-posed and to correctly solve the Bellman-Isaacs equation with an appropriate numeric scheme

Suggested Citation

  • Nikolay A Andreev, 2017. "Boundedness of the Value Function of the Worst-Case Portfolio Selection Problem with Linear Constraints," HSE Working papers WP BRP 59/FE/2017, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:59/fe/2017
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    References listed on IDEAS

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    1. 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.
    2. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    3. 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 247-257, August.
    4. Deng, Xiao-Tie & Li, Zhong-Fei & Wang, Shou-Yang, 2005. "A minimax portfolio selection strategy with equilibrium," European Journal of Operational Research, Elsevier, vol. 166(1), pages 278-292, October.
    5. 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.
    6. Nikolay A. Andreev, 2015. "Worst-Case Approach To Strategic Optimal Portfolio Selection Under Transaction Costs And Trading Limits," HSE Working papers WP BRP 45/FE/2015, National Research University Higher School of Economics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    portfolio selection; Bellman-Isaacs equation; stochastic dynamic programming; value function; worst-case optimization;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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