Rupak Bhattacharyya

Fuzzy mean-variance-skewness portfolio selection models by interval analysis

In portfolio selection problem, the expected return, risk, liquidity etc. cannot be predicted precisely. The investor generally makes his portfolio decision according to his experience and his economic wisdom. So, deterministic portfolio selection is not a good choice for the investor. In most of the recent works on this problem, fuzzy set theory is widely used to model the problem in uncertain environments. This paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean-variance (MV) portfolio selection model into mean-variance-skewness (MVS) model with consideration of transaction cost. In addition, some other criteria like short and long term returns, liquidity, dividends, number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered. Three different models have been proposed by defining the future financial market optimistically, pessimistically and in the combined form to model the fuzzy MVS portfolio selection problem. In order to solve the models, fuzzy simulation (FS) and elitist genetic algorithm (EGA) are integrated to produce a more powerful and effective hybrid intelligence algorithm (HIA). Finally, our approaches are tested on a set of stock data from Bombay Stock Exchange (BSE).

Fuzzy R&D portfolio selection of interdependent projects

Global competition of markets has forced firms to invest in targeted R&D projects so that resources can be focused on successful outcomes. A number of options are encountered to select the most appropriate projects in an R&D project portfolio selection problem. The selection is complicated by many factors, such as uncertainty, interdependences between projects, risk and long lead time, that are difficult to measure. Our main concern is how to deal with the uncertainty and interdependences in project portfolio selection when evaluating or estimating future cash flows. This paper presents a fuzzy multi-objective programming approach to facilitate decision making in the selection of R&D projects. Here, we present a fuzzy tri-objective R&D portfolio selection problem which maximizes the outcome and minimizes the cost and risk involved in the problem under the constraints on resources, budget, interdependences, outcome, projects occurring only once, and discuss how our methodology can be used to make decision support tools for optimal R&D project selection in a corporate environment. A case study is provided to illustrate the proposed method where the solution is done by genetic algorithm (GA) as well as by multiple objective genetic algorithm (MOGA).

Uncertainty theory based multiple objective mean-entropy-skewness stock portfolio selection model with transaction costs

PurposeThe aim of this paper is to develop a mean-entropy-skewness stock portfolio selection model with transaction costs in an uncertain environment.MethodsSince entropy is free from reliance on symmetric probability distributions and can be computed from nonmetric data, it is more general than others as a competent measure of risk. In this work, returns of securities are assumed to be uncertain variables, which cannot be estimated by randomness or fuzziness. The model in the uncertain environment is formulated as a nonlinear programming model based on uncertainty theory. Also, some other criteria like short-and long-term returns, dividends, number of assets in the portfolio, and the maximum and minimum allowable capital invested in stocks of any company are considered. Since there is no efficient solution methodology to solve the proposed model, assuming the returns as some special uncertain variables, the original portfolio selection model is transformed into an equivalent deterministic model, which can be solved by any state-of-the-art solution methodology.ResultsThe feasibility and effectiveness of the proposed model is verified by a numerical example extracted from Bombay Stock Exchange, India. Returns are considered in the form of trapezoidal uncertain variables. A genetic algorithm is used for simulation.ConclusionsThe efficiency of the portfolio is evaluated by looking for risk contraction on one hand and expected return and skewness augmentation on the other hand. An empirical application has served to illustrate the computational tractability of the approach and the effectiveness of the proposed algorithm.

Mean-Entropy-Skewness Fuzzy Portfolio Selection by Credibility Theory Approach

In this paper fuzzy mean-entropy-skewness models are proposed for optimal portfolio selection. Entropy is favored as a measure of risk as it is free from dependence on symmetric probability distribution. Credibility theory is applied to evaluate fuzzy mean, skewness and entropy. Hybrid intelligence algorithm is used for simulation. Numerical examples are given in favor of each of the models.

Methods of Evaluation and Extraction of Membership Functions--Review with a New Approach

In fuzzy mathematics, evaluation of membership function is still a problem, as the methods for this purpose do not hold well in all aspects. The purpose of this work is to assemble and to draw an overview of them. In addition, this work consists of a new approach, which may lead to a new way. The approach is from numerical point of view with the help of statistics. There are two methods, namely (i) modified Newtons divided difference method and (ii) modified Lagranges interpolation method

Optimization Of Mean‐Semivariance‐Skewness Portfolio Selection Model In Fuzzy Random Environment

The purpose of the paper is to construct a mean‐semivariance‐skewness portfolio selection model in fuzzy random environment. The objective is to maximize the skewness with predefined maximum risk tolerance and minimum expected return. Here the security returns in the objectives and constraints are assumed to be fuzzy random variables in nature and then the vagueness of the fuzzy random variables in the objectives and constraints are transformed into fuzzy variables which are similar to trapezoidal numbers. The newly formed fuzzy model is then converted into a deterministic optimization model. The feasibility and effectiveness of the proposed method is verified by numerical example extracted from Bombay Stock Exchange (BSE). The exact parameters of fuzzy membership function and probability density function are obtained through fuzzy random simulating the past dates.

Fuzzy Random λ‐Mean SAD Portfolio Selection Problem: An Ant Colony Optimization Approach

To reach the investment goal, one has to select a combination of securities among different portfolios containing large number of securities. Only the past records of each security do not guarantee the future return. As there are many uncertain factors which directly or indirectly influence the stock market and there are also some newer stock markets which do not have enough historical data, experts’ expectation and experience must be combined with the past records to generate an effective portfolio selection model. In this paper the return of security is assumed to be Fuzzy Random Variable Set (FRVS), where returns are set of random numbers which are in turn fuzzy numbers. A new λ‐Mean Semi Absolute Deviation (λ‐MSAD) portfolio selection model is developed. The subjective opinions of the investors to the rate of returns of each security are taken into consideration by introducing a pessimistic‐optimistic parameter vector λ. λ‐Mean Semi Absolute Deviation (λ‐MSAD) model is preferred as it follows absolute...

Merit Evaluation Of Competitors In Debate And Recitation Competitions By Fuzzy Approach

Co‐curricular activities have a great importance in students’ life, especially to grow their personality and communication skills. In different process of evaluating competitors in such competitions, generally crisp techniques are used. In this paper, we introduce a new fuzzy set theory based method of evaluation of competitors in co‐curricular activities like debate and recitation competitions. The proposed method is illustrated by two examples.