Wyniki wyszukiwania - BazTech

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The Application of genetic algorithms for the selection of WSE companies in Warsaw for the investment portfolio

Basiura Beata, Motyczyńska Joanna

Decision Making in Manufacturing and Services

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2020

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Vol. 14, no. 1

91--126

EN

Portfolio analysis is a tool particularly intended for investors. Risk assessment and risk specification make the investor able to properly diversify and offset the portfolio. Broadly speaking, there are multiple tools destined for building up an efficient set of portfolios. One of them is Markowitz’s model theory postulating building up a portfolio determined on the basis of equilibrium between expected profit level as well as accepted level of risk assessment. In the context of this paper, the objective is to shed some light on creating investment portfolios based on either Markowitz's portfolio theory or evolutionary algorithm. The simulation based methods for building up a portfolio of approximately 40-50 companies listed out in the primary marketof the Warsaw Stock Exchange using the selection function proposed in the BA thesis were presented. Portfolio profit values have been evaluated in a dynamically shifted time window. The conducted analysis showed shifts in the economy at certain periods of time. The implemented genetic algorithms smoothly handled the optimization with a relatively short processing time of the task result.

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An interactive compromise programming for portfolio investment problem

Karelkina Olga

Control and Cybernetics

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2020

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Vol. 49, No. 2

193--210

EN

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.

3

A condition for asset redundancy in the mean-variance model of portfolio investment

Juszczuk Przemysław, Kaliszewski Ignacy, Miroforidis Janusz, Podkopaev Dmitry

Control and Cybernetics

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2020

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Vol. 49, No. 2

179--191

EN

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.

4

Random approximations in multiobjective programming - with an application to portfolio optimization with shortfall constraints

Vogel S.

Control and Cybernetics

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1999

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Vol. 28, no 4

703-724

EN

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.

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Multiobjective duality for the Markowitz portfolio optimization problem

Wanka G.

Control and Cybernetics

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1999

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Vol. 28, no 4

691-702

EN

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.