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1

Orderings and risk probability functionals in portfolio theory

Ortobelli S., Rachev S., Shalit H., Fabozzi F. J.

Probability and Mathematical Statistics

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2008

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Vol. 28, Fasc. 2

203--234

EN

This paper studies and describes stochastic orderings of risk/reward positions in order to define in a natural way risk/reward measures consistent/isotonic to investors’ preferences. We begin by discussing the connection between the theory of probability metrics, risk measures, distributional moments, and stochastic orderings. Then we examine several classes of orderings which are generated by risk probability functionals. Finally, we demonstrate how further orderings could better specify the investor’s attitude toward risk.

2

Multicriteria aiding of decision - makers in the process of selecting projects applying for cofinancing from the European Union

Górecka D.

Foundations of Computing and Decision Sciences

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2008

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Vol. 33, No. 1

25-42

EN

Since the enlargement of the European Union in 2004 Poland has got a great opportunity to benefit from the European Union structural funds intended for supporting restructuring and modernisation of the weaker regions of EU member countries. One of the conditions of not missing this opportunity is rational allocation of the financial means provided by the funds that depends among others on proper choice of projects that are going to be co-financed. In order to aid the decision-makers in this important and difficult task the multiple criteria analysis techniques can be applied, especially these ones based on the outranking relation. As the empirical example of above-mentioned problem the application of stochastic dominance rules and multicriteria methods from ELECTRE and PROMETHEE families to selecting projects applying for co-financing from the European Regional Development Fund and reported on Measure 1.2 Environmental protection infrastructure is going to be presented1.

3

Composite semi-infinite optimization

Dentcheva D., Ruszczyński A.

Control and Cybernetics

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2007

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Vol. 36, no 3

633-646

EN

We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to non-convex stochastic optimization problems with stochastic dominance constraints, generalizing earlier results.

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Parametryczna dominacja probabilistyczna-model wielokryterialny

Zawisza M.

Badania Operacyjne i Decyzje

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2005

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nr 3-4

129-145

PL

W pracy przedstawiono wybrane elementy teorii dominacji stochastycznych i dominacji probabilistycznej oraz ich wykorzystanie w wielokryterialnych problemach wspomagania decyzji. Pierwsza część pracy zawiera definicje dominacji stochastycznych. Najistotniejsza część pracy to rozdział drugi. Podano w nim definicję dominacji probabilistycznej oraz jej modyfikację, zaproponowaną przez autora. Wykorzystując własności dominacji probabilistycznej, autor wprowadził nową wielkość dla wyznaczania dominacji probabilistycznej - bmax. Określa ona maksymalny poziom prawdopodobieństwa, dla którego zachodzi relacja dominacji probabilistycznej pomiędzy dwiema zmiennymi losowymi. Autor definiuje parametryczną dominację probabilistyczną PPD, wykorzystując bmax oraz nowy parametr b*. Wprowadzenie parametru b* do definicji dominacji probabilistycznej pozwala na określenie siły dominacji. W ostatniej, trzeciej, części opracowania zaprezentowano wykorzystanie parametrycznej dominacji probabilistycznej PPD do rozwiązywania problemów wielokryterialnych. Zmieniając wartość parametru b* w modelu, uwypuklamy albo dominację stochastyczną (odnosząc się do postaw decydenta wobec ryzyka), albo dominację probabilistyczną.

EN

The paper shows the chosen elements of stochastic dominance and probabilistic dominance theory, as well as their utilization in multicriteria decision support problems. The first part of the paper contains definitions of stochastic dominations. The second part is most essential. It describes the probabilistic dominance definition and its modification made by the author. Using the property of probabilistic dominance the author proposes bmax, which defines the maximum level of probability. Next, the author defines the Parametric Probablistic Dominance PPD using bmax as well as the new parameter b *, which allows the strength of the domination to be chosen. The third part of the study shows the utilization of parametric probabilistic dominance to solve multicriteria decision support problem. By changing the value of parameter b * in our multicriteria model we can put more strength on the stochastic dominance, or on the probabilistic dominance.

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Interactive approach in multicriteria analysis based on stochastic dominance

Nowak M.

Control and Cybernetics

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2004

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Vol. 33, no 3

463-476

EN

The paper considers a discrete stochastic multicriteria problem. This problem can be denned by a finite set of actions A, a set of attributes X and a set of evaluations E. It is assumed that the performance probability distributions for each action on each attribute are known. A new procedure for such a problem is proposed. It is based on two concepts: stochastic dominance and interactive approach. Stochastic dominance is employed for comparing evaluations of actions with respect, to attributes. The STEM methodology is employed in the dialogue procedure between decision maker and decision model. In each step a candidate action a_i is generated. The decision maker examines evaluations of a_i, with respect to attributes and selects the one that satisfies him/her. Then the decision maker defines the limit of concessions, which can be made on average evaluations with respect to this attribute. The procedure continues until a satisfactory action is found.