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1
Content available A weighted-sum mixed integer program for bi--objective dynamic portfolio optimization
100%
Sawik B.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
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2009
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tom T. 13, z. 2
563-571
EN
The portfolio selection problem presented in this paper is formulated as a bi-objective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize the weighted difference of the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used.
PL
Celem optymalizacji jest dynamiczne wyznaczenie portfela 0 maksymalnej oczekiwanej stopie zwrotu, dla której prawdopodobieństwo wartości zagrożonej zwrotu mniejszej od zadanej wartości będzie nie większe od minimalizowanego progu. Model sformułowano jako dwukryterialne zadanie programowania całkowitoliczbowego z ważoną funkcją celu. Zastosowano metody programowania całkowitoliczbowego mieszanego. Przedstawiono wyniki eksperymentów obliczeniowych z użyciem dziennych danych z GPW w Warszawie.
2
Content available Conditional value-at-risk and value-at-risk for portfolio optimization model with weighting approach
100%
Sawik B.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
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2011
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tom T. 15, z. 2
429-434
EN
This paper presents a multi-objective portfolio models with the expected return as a performance measure and the expected worst-case return as a risk measure. The problem objective is to allocate the wealth on different securities to optimize the portfolio expected return. This portfolio approach has allowed the two popular in financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided.
PL
W artykule przedstawiono model wielokryterialnej optymalizacji portfelowej z ważoną funkcją celu. Celem optymalizacji jest wyznaczenie portfela o maksymalnej oczekiwanej stopie zwrotu przy ryzyku wyznaczonym za pomocą miar CVaR oraz VaR. Przedstawiono wyniki eksperymentów obliczeniowych z użyciem danych z GPW w Warszawie.
3
Content available A reference point approach to bi-objective dynamic portfolio optimization
100%
Sawik B.
Decision Making in Manufacturing and Services
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2009
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tom Vol. 3, no. 1-2
73-85
EN
The portfolio selection problem presented in this paper is formulated as a bi-objective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize by reference point method the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used.
4
Content available remote A three stage lexicographic approach for multi-criteria portfolio optimization by mixed integer programming
100%
Sawik B.
Przegląd Elektrotechniczny
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2008
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tom R. 84, nr 9
108-112
EN
The portfolio optimization problem is formulated as multi-objective mixed integer program. The problem considered is based on a single period model of investment. The problem objective is to allocate wealth on different assets to maximize the weighted difference of portfolio expected return, the threshold of the probability that the return is not less than required level and the amount of wealth to be invested. The results of some computational experiments modeled after a real data from the Warsaw Stock Exchange are reported.
PL
W artykule przedstawiono wielokryterialny model optymalizacji portfelowej wraz z trójetapowym podejściem lksykalno-graficznym. Celem optymalizacji jest wyznaczenie portfela o maksymalnej oczekiwanej stopie zwrotu, dla której prawdopodobieństwo wartości zagrożonej zwrotu (VaR) przy ryzyku mniejszym od zadanej wartości będzie nie większe od zadanego lub minimalizowanego progu. Przedstawiono wyniki eksperymentów obliczeniowych dla danych zaczerpniętych z GPW w Warszawie.
5
Content available remote Bi-Criteria Portfolio Optimization Models with Percentile and Symmetric Risk Measures by Mathematical Programming
100%
Sawik B.
Przegląd Elektrotechniczny
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2012
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tom R. 88, nr 10b
176-180
EN
The purpose of this paper is to compare three different bi-criteria portfolio optimization models. The first model is constructed with the use of percentile risk measure Value-at-Risk and solved by mixed integer programming. The second one is constructed with the use of percentile risk measure Conditional Value-at-Risk and solved by linear programming. The third one is constructed with the use of a symmetric measure of risk - variance of return - as in the Markowitz portfolio and solved by quadratic programming. Computational experiments are conducted for bi-criteria portfolio stock exchange investments. The results obtained prove, that the bi-objective portfolio optimization models with Value-at-Risk and Conditional Value-at-Risk could be used to shape the distribution of portfolio returns. The decision maker can assess the value of portfolio return and the risk level, and can decide how to invest in a real life situation comparing with ideal (optimal) portfolio solutions. The proposed scenario-based portfolio optimization problems under uncertainty, formulated as a bi-objective linear, mixed integer or quadratic program are solved using commercially available software (AMPL/CPLEX) for mathematical programming.
PL
W pracy zaprezentowano problem portfelowy, dla którego zaproponowane zostały trzy dwukryterialne modele optymalizacji. W kazdym z zaimplementowanych modeli funkcja celu jest wazona suma dwóch kryteriów, które podlegają optymalizacji dla konkretnego portfela. W pierwszym modelu z warunkową wartoscią zagrozoną zwrotu (Conditional Value-at-Risk) kryteria decyzyjne to maksymalizacja CVaR i przewidywanego zwrotu portfela. W drugim modelu z wartoscią zagrozoną zwrotu (Value-at-Risk) minimalizowane jest prawdopodobienstwo ryzyka straty oraz maksymalizacja oczekiwanego zwrotu z portfela. Trzeci model to omawiany szeroko w literaturze model portfela Markowitza zmodyfikowany tak, by funkcja kryterialna była wazona sumą kryteriów i minimalizowała ryzyko portfela zdefiniowanego jako macierz kowariancji historycznych zwrotów oraz maksymalizowała przewidywany zwrot portfela. Modele te zostały zaimplementowane: w pierwszym - uzywając metody programowania mieszanego całkowitoliczbowego, a w drugi i trzeci z uzyciem programowania liniowego i kwadratowego. Efektywnosc zaproponowanych modeli została zweryfikowana eksperymentalnie, zwracając szczególną uwagę na czas obliczen oraz przewidywany zwrot portfela. Zamieszczono wyniki eksperymentów obliczeniowych przeprowadzonych z zastosowaniem optymizatora CPLEX i jezyka modelowania algebraicznego AMPL.
6
Content available A reference point method to triple-objective assignment of supporting services in a healthcare institution
100%
Sawik B.
Decision Making in Manufacturing and Services
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2010
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tom Vol. 4, no. 1-2
37-46
EN
This paper presents an application of mixed integer programming model for optimal allocation of workers among supporting services in a hospital. The services include logistics, inventory management, financial management, operations management, medical analysis, etc. The optimality criterion of the problem is to minimize operational costs of supporting services subject to some specific constraints. The constraints represent specific conditions for resource allocation in a hospital. The overall problem is formulated as a triple-objective assignment model, where the decision variables represent the assignment of people to various jobs. A reference point approach with the Chebyshev metric is applied for the problem solution. The results of computational experiments modeled on a real data from a hospital in Lesser Poland are reported.
7
Content available A bi-objective portfolio optimization with conditional value-at-risk
100%
Sawik B.
Decision Making in Manufacturing and Services
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2010
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tom Vol. 4, no. 1-2
47-69
EN
This paper presents a bi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a bi-objective linear program. Numerical examples based on 1000, 3500 and 4020 historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that the proposed linear programming approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.
8
Content available The Effect of Environmental Criteria on Locating a Biorefinery: a Green Facility Location Problem
51%
Serrano-Hernandez A. , Faulin J. , Belloso J. , Sawik B.
Decision Making in Manufacturing and Services
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2017
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tom Vol. 11, no. 1-2
19--30
EN
Underestimating facility location decisions may penalize business performance over the time. These penalties have usually been studied from the economic point of view, analyzing its impact on profitability. Additionally, the concern about obtaining sustainability is gaining importance, leading to a search for renewable energy sources to reduce greenhouse gas emissions. However, little attention has been paid to choosing a location considering environmental criteria. Thus, this work aims at determining a biorefinery location considering its impacts on natural resources. Therefore, a mixed integer linear programming (MILP) model has been developed, taking into account crop location and biomass production seasonality to obtain a proper location that minimizes environmental impact.
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