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    Wyświetlanie 1-4 z 4
    Tytuł:
    Multiobjective duality for the Markowitz portfolio optimization problem
    Autorzy:
    Wanka, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/206011.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dualność
    optymalizacja
    duality
    expected return
    investment
    Markowitz model
    optimality conditions
    portfolio optimization
    Opis:
    The classical Markowitz approach to portfolio selection leads to a biobjective optimization problem where the objectives are the expected return and the variance of a portfolio. In this paper a biobjective dual optimization problem to the Markowitz portfolio optimization problem is introduced and analyzed. For the Markowitz problem and its dual, weak and strong vector duality assertions are derived. The optimality conditions are also verified.
    Źródło:
    Control and Cybernetics; 1999, 28, 4; 691-702
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A condition for asset redundancy in the mean-variance model of portfolio investment
    Autorzy:
    Juszczuk, Przemysław
    Kaliszewski, Ignacy
    Miroforidis, Janusz
    Podkopaev, Dmitry
    Powiązania:
    https://bibliotekanauki.pl/articles/2050025.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    modern portfolio theory
    Markowitz model
    meanvariance portfolio optimization
    asset redundancy
    problem size
    Opis:
    The mean-variance approach to portfolio investment exploits the fact that the diversification of investments by combination of different assets in one portfolio allows for reducing the financial risks significantly. The mean-variance model is formulated as a bi-objective optimization problem with linear (expected return) and quadratic (variance) objective functions. Given a set of available assets, the investor searches for a portfolio yielding the most preferred combination of these objectives. Naturally, the search is limited to the set of non-dominated combinations, referred to as the Pareto front. Due to the globalization of financial markets, investors nowadays have access to large numbers of assets. We examine the possibility of reducing the problem size by identifying those assets, whose removal does not affect the resulting Pareto front, thereby not deteriorating the quality of the solution from the investor’s perspective. We found a sufficient condition for asset redundancy, which can be verified before solving the problem. This condition is based on the possibility of reallocating the share of one asset in a portfolio to another asset without deteriorating the objective function values. We also proposed a parametric relaxation of this condition, making it possible to removemore assets for a price of a negligible deterioration of the Pareto front. Computational experiments conducted on five real-world problems have demonstrated that the problem size can be reduced significantly using the proposed approach.
    Źródło:
    Control and Cybernetics; 2020, 49, 2; 179-191
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An interactive compromise programming for portfolio investment problem
    Autorzy:
    Karelkina, Olga
    Powiązania:
    https://bibliotekanauki.pl/articles/2050029.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    modern portfolio theory
    Markowitz model
    meanvariance portfolio optimization
    interactive multicriteria optimization
    parameterized achievement scalarizing functions
    Opis:
    This paper addresses an approach for solving multicriteria portfolio investment problem. The original Markowitz mean-variance model is formulated as a problem of bi-objective optimization with linear and quadratic objective functions. In the current work, this model is extended by introducing a new objective, reflecting asset properties that are useful for the portfolio allocation process. A method based on parameterized achievement scalarizing function is applied to produce Pareto optimal portfolios. A mathematical programming formulation that allows for solving the problem with conventional optimization methods is presented. In addition, a method of reflecting the decision maker’s preferences by means of changing the weights in the achievement scalarizing functions is introduced. A decision making process is simulated for the three-objective portfolio optimization problem.
    Źródło:
    Control and Cybernetics; 2020, 49, 2; 193-210
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Random approximations in multiobjective programming - with an application to portfolio optimization with shortfall constraints
    Autorzy:
    Vogel, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/205947.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    aproksymacja stochastyczna
    optymalizacja
    prawdopodobieństwo
    programowanie matematyczne
    stabilność
    estimated quantities
    Markowitz model
    multiobjective progranming
    portfolio
    probabilistic constraints
    stability
    Opis:
    Decision makers often heave to deal with a programming problem vhere some of the quantities are unknown. They will usually estimate these quantities and solve the problem as it then appears - the "approximate problem". Thus, there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. The paper summarizes such results for multiobjective programming problems. The results ase illustrated by means of the Markowitz model of portfolio optimization. In order to show how probabilistic constraints may be dealt with using this framework, a shortfall constraint is taken into account.
    Źródło:
    Control and Cybernetics; 1999, 28, 4; 703-724
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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