Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.

We use in this chapter the viability/capturability approach for studying the problem of dynamic valuation and management of a portfolio with transaction costs in the framework of tychastic control systems (or dynamical games against nature) instead of stochastic control systems. Indeed, the very definition of the guaranteed valuation set can be formulated directly in terms of guaranteed viable-capture basin of a dynamical game. Hence, we shall “compute” the guaranteed viable-capture basin and find a formula for the valuation function involving an underlying criterion, use the tangential properties of such basins for proving that the valuation function is a solution to Hamilton-Jacobi-Isaacs partial differential equations. We then derive a dynamical feedback providing an adjustment law regulating the evolution of the portfolios obeying viability constraints until it achieves the given objective in finite time. We shall show that the Pujal—Saint-Pierre viability/capturability algorithm applied to this specific case provides both the valuation function and the associated portfolios.dynamic games; dynamic valuation; tychastic control systems; management of portfolio;

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

A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market

[EN] This paper extends the stochastic mean-semivariance model to a fuzzy multiobjective model, where apart from return and risk, also liquidity is considered to measure the performance of a portfolio. Uncertainty of future return and liquidity of each asset are modeled using L-R type fuzzy numbers that belong to the power reference function family. The decision process of this novel approach takes into account not only the multidimensional nature of the portfolio selection problem but also realistic constraints by investors. Particularly, it optimizes the expected return, the semivariance and the expected liquidity of a given portfolio, considering cardinality constraint and upper and lower bound constraints. The constrained portfolio optimization problem resulting is solved using the algorithm NSGA-II. As a novelty, in order to select the optimal portfolio, this study defines the credibilistic Sortino ratio as the ratio between the credibilistic risk premium and the credibilistic semivariance. An empirical study is included to show the effectiveness and efficiency of the model in practical applications using a data set of assets from the Latin American Integrated Market.García García, F.; Gonzalez-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J. (2020). A multiobjective credibilistic portfolio selection model. Empirical study in the Latin American Integrated Market. Enterpreneurship and Sustainability Issues. 8(2):1027-1046. https://doi.org/10.9770/jesi.2020.8.2(62)S102710468

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

The Financial Crisis Impact on the Composition of an Optimal Portfolio in the Stock Market - Study Applied to Portuguese Index PSI 20

In order to maximize their utility function, investors select some assets over others, choosing the portfolio that will allow them to maximize their wealth. Each asset is chosen considering the relationship between the risk of that particular investment (usually measured by variance) - and the profitability it can offer, as well as the risk between this and other assets (measured by covariance). The purpose of this study consisted of constructing the minimum variance portfolio, using data from the PSI-20 (2008-2016) representative asset quotation, where investors are risk reluctant and wish to minimize risk while maintaining the same level of profitability, or on the other hand, maintaining the same level of risk but maximizing expected profit. In order to do this, a comparison of the optimal portfolio in 2004-2017 was carried out, compared to the minimum variance portfolio after the financial crisis (2008-2016). The method used to estimate each asset’s expected profitability that makes up the PSI-20 consists of extracting the obtained historical quotations. The optimal portfolio composition, in the period after the financial crisis, shows that the energy sector has an optimal portfolio weight reduction of 39.15%, that the big distribution sector (23.85%) was introduced into the portfolio and by last, the industrial sector stands its ground in the composition of the optimal portfolio.info:eu-repo/semantics/publishedVersio