Strict Solution Method for Linear Programming Problem with Ellipsoidal Distributions under Fuzziness

This paper considers a linear programming problem with ellipsoidal distributions including fuzziness. Since this problem is not well-defined due to randomness and fuzziness, it is hard to solve it directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed model is transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve the main problem analytically and efficiently due to nonlinear programming, the solution method is constructed introducing an appropriate parameter and performing the equivalent transformations

Improved Constrained Portfolio Selection Model using Particle Swarm Optimization

Objective: The main objective of this study is to improve the extended Markowitz mean-variance portfolio selection model by introducing a new constraint known as expert opinion practicable for portfolio selection in real-life situation. Methods: This new extended model consists of four constraints namely: bounds on holdings, cardinality, minimum transaction lots, and expert opinion. The first three constraints have been presented in other researches in literature. The fourth constraint introduced in this study is an essential parameter in making and guiding a realistic portfolio selection. To solve this new extended model an efficient heuristic method of Particle Swarm Optimization (PSO) was engaged with existing benchmark data in the literature. Results: The outcome of the computational results obtained in this study with the new extended Markowitz mean-variance portfolio selection model proposed in this study and solved with PSO showed an improved performance over existing algorithm in particular GA in different instances of the data set used. Conclusion: The study evolves a new extended portfolio selection model and the findings

Portfolio Selection Problems with Normal Mixture Distributions Including Fuzziness

In this paper, several portfolio selection problems with normal mixture distributions including fuzziness are proposed. Until now, many researchers have proposed portfolio models based on the stochastic approach, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, the model including normal mixture distributions with fuzzy numbers has not been proposed yet. Our proposed problems are not well-defined problems due to randomness and fuzziness. Therefore, setting some criterions and introducing chance constrains, main problems are transformed into deterministic programming problems. Finally, we construct a solution method to obtain a global optimal solution of the problem

A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution

A Comparative Analysis of an Interior-point Method and a Sequential Quadratic Programming Method for the Markowitz Portfolio Management Problem

In this paper, I give a brief introduction of the general optimization problem as well as the convex optimization problem. The portfolio selection problem, as a typical type of convex optimization problem, can be easily solved in polynomial time. However, when the number of available stocks in the portfolio becomes large, there might be a significant difference in the running time of different polynomial-time solving methods. In this paper, I perform a comparative analysis of two different solving methods and discuss the characteristics and differences

High-low Strategy of Portfolio Composition using Evolino RNN Ensembles

trategy of investment is important tool enabling better investor's decisions in uncertain finance market. Rules of portfolio selection help investors balance accepting some risk for the expectation of higher returns. The aim of the research is to propose strategy of constructing investment portfolios based on the composition of distributions obtained by using high–low data. The ensemble of 176 Evolino recurrent neural networks (RNN) trained in parallel investigated as an artificial intelligence solution, which applied in forecasting of financial markets. Predictions made by this tool twice a day with different historical data give two distributions of expected values, which reflect future dynamic exchange rates. Constructing the portfolio, according to the shape, parameters of distribution and the current value of the exchange rate allows the optimization of trading in daily exchange-rate fluctuations. Comparison of a high-low portfolio with a close-to-close portfolio shows the efficiency of the new forecasting tool and new proposed trading strategy

Portfolio Optimization Efficiency Test Considering Data Snooping Bias

Background: In the portfolio optimization area, most of the research is focused on in-sample portfolio optimization. One may ask a rational question of what the efficiency of the portfolio optimization strategy is and how to measure it. Objectives: The objective of the paper is to propose the approach to measuring the efficiency of the portfolio strategy based on the hypothesis inference methodology and considering a possible data snooping bias. The proposed approach is demonstrated on the Markowitz minimum variance model and the fuzzy probabilities minimum variance model. Methods/Approach: The proposed approach is based on a statistical test. The null hypothesis is that the analysed portfolio optimization strategy creates a portfolio randomly, while the alternative hypothesis is that an optimized portfolio is created in such a way that the risk of the portfolio is lowered. Results: It is found out that the analysed strategies indeed lower the risk of the portfolio during the market’s decline in the global financial crisis and in 94% of the time in the 2009-2019 period. Conclusions: The analysed strategies lower the risk of the portfolio in the out-of-sample period

Portfel wieloskładnikowy z nieprecyzyjną wartością bieżącą daną trapezoidalną liczby rozmytej

The article includes an analysis of a multiple asset portfolio, paying special attention to an imprecision risk, burdening the component instruments. The imprecision of decision premises is modeled in the imprecisely stated present value of portfolio assets, given subjectively by the investor in the form of trapezoidal fuzzy numbers. Next, for each asset and consisting portfolio we define imprecision measures appointed based on a fuzzy discounting factor. Analyzed theoretical model takes into account not only rational premises of a decision, but also allows for an inclusion of behavioral, technical and technological factors. During the performed research, relations between imprecision risk measures of assets and portfolio were found. Imprecision risk assessments are computed based on energy and entropy measures. Also, a case study is given, presenting mechanics of the model and methods of calculating risk measures. Performed analysis led to formulating some conclusions about the form and behavior of imprecision risk burdening a portfolio.Praca zawiera analizę portfela wieloskładnikowego pod kątem ryzyka nieprecyzyjności. Nieprecyzyjność przesłanek decyzyjnych jest modelowana nieprecyzyjnym określeniem wartości bieżącej instrumentów składowych portfela podanej subiektywnie przez inwestora w postaci trapezoidalnej liczby rozmytej. Dla poszczególnych składników oraz skonstruowanego z nich portfela określone są miary obarczającej je nieprecyzyjności, badanej na podstawie rozmytych czynników dyskontujących. Analizowany model teoretyczny, oprócz przesłanek racjonalnych, uwzględnia czynniki behawioralne oraz techniczne i technologiczne wpływające na decydenta. Oceny ryzyka nieprecyzyjności rozważanego portfela dokonano przy pomocy miar energii i entropii. Przedstawiono również studium przypadku prezentujące sposób działania modelu i metody obliczania miar nieprecyzyjności. Na podstawie przeprowadzonych badań sformułowano wnioski dotyczące postaci i zachowania ryzyka nieprecyzyjności portfela