Forecasting portfolio returns using weighted fuzzy time series methods

We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and ambiguity of a fuzzy number.We incorporate our proposals into classical fuzzy time series methods and analyze their effectiveness compared with classical weighted fuzzy time series models, using historical returns on assets from the Spanish stock market. When our weighted FTS proposals are used to point-wise forecast portfolio returns the one-step ahead accuracy is improved, also with respect to non-fuzzy forecasting methods.     

On the possibilistic mean value and variance of multiplication of fuzzy numbers

In this paper, we introduce the definitions of the possibilistic mean, variance and covariance of multiplication of fuzzy numbers, and show some properties of these definitions. Then, we apply these definitions to build the possibilistic models of portfolio selection under the situations involving uncertainty over the time horizon, by considering the portfolio selection problem from the point of view of possibilistic analysis. Moreover, numerical experiments with real market data indicate that our approach results in better portfolio performance.     

Fuzzy portfolio model with different investor risk attitudes

We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.     

A class of possibilistic portfolio selection model with interval coefficients and its application

Because of the existence of non-stochastic factors in stock markets, several possibilistic portfolio selection models have been proposed, where the expected return rates of securities are considered as fuzzy variables with possibilistic distributions. This paper deals with a possibilistic portfolio selection model with interval center values. By using modality approach and goal attainment approach, it is converted into a nonlinear goal programming problem. Moreover, a genetic algorithm is designed to obtain a satisfactory solution to the possibilistic portfolio selection model under complicated constraints. Finally, a numerical example based on real world data is also provided to illustrate the effectiveness of the genetic algorithm.     

Fuzzy portfolio selection model with real features and different decision behaviors

In the ever changing financial markets, investor’s decision behaviors may change from time to time. In this paper, we consider the effect of investor’s different decision behaviors on portfolio selection in fuzzy environment. We present a possibilistic mean-semivariance model for fuzzy portfolio selection by considering some real investment features including proportional transaction cost, fixed transaction cost, cardinality constraint, investment threshold constraints, decision dependency constraints and minimum transaction lots. To describe investor’s different decision behaviors, we characterize the return rates on securities by LR fuzzy numbers with different shape parameters in the left- and right-hand reference functions. Then, we design a novel hybrid differential evolution algorithm to solve the proposed model. Finally, we provide a numerical example to illustrate the application of our model and the effectiveness of the designed algorithm.     

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.     

模糊环境中带交易费用的投资组合策略问题

由于金融市场是波动的,风险资产的预期收益率由于很多不确定性是很难估计的,本文考虑预期收益率是可能性分布(模糊数),并且在此基础上用模糊数的可能性均值表示投资组合的收益,用模糊数的平均绝对偏差表示风险,考虑了交易费用后,得到投资组合模型,最后给出了数值计算的例子.     

基于模糊收益率的组合投资模型

本文考虑了收益率为模糊数的投资组合选择问题,利用模型约束简化方差约束,建立了投资组合选择的模糊线性规划模型,然后引进模糊期望把模糊线性规划问题化为普通参数线性规划问题,最后给出了一个数值算例.     

A cutting plane algorithm for MV portfolio selection model

This paper deals with a portfolio selection problem with fuzzy return rates. A possibilistic mean variance (FMVC) portfolio selection model was proposed. The possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory. For such problems there are no special standard algorithms. We propose a cutting plane algorithm to solve (FMVC). The nonlinear programming problem can be solved by sequence linear programming problem. A numerical example is given to illustrate the behavior of the proposed model and algorithm.     

A multi-objective evolutionary optimization approach for an integrated location-inventory distribution network problem under vendor-managed inventory systems

This paper develops a λ mean-hybrid entropy model to deal with portfolio selection problem with both random uncertainty and fuzzy uncertainty. Solving this model provides the investor a tradeoff frontier between security return and risk. We model the security return as a triangular fuzzy random variable, where the investor’s individual preference is reflected by the pessimistic-optimistic parameter λ. We measure the security risk using the hybrid entropy in this model. Algorithm is developed to solve this bi-objective portfolio selection model. Beside, a numerical example is also presented to illustrate this approach.     

A portfolio selection model using fuzzy returns

We study a static portfolio selection problem, in which future returns of securities are given as fuzzy sets. In contrast to traditional analysis, we assume that investment decisions are not based on statistical expectation values, but rather on maximal and minimal potential returns resulting from the so-called α-cuts of these fuzzy sets. By aggregating over all α-cuts and assigning weights for both best and worst possible cases we get a new objective function to derive an optimal portfolio. Allowing for short sales and modelling α-cuts in ellipsoidal shape, we obtain the optimal portfolio as the unique solution of a simple optimization problem. Since our model does not include any stochastic assumptions, we present a procedure, which turns the data of observable returns as well as experts’ expectations into fuzzy sets in order to quantify the potential future returns and the investment risk.     

Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications

We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem. B.K. Pagnoncelli’s research was supported by CAPES and FUNENSEG. S. Ahmed’s research was partly supported by the NSF Award DMI-0133943. A. Shapiro’s research was partly supported by the NSF Award DMI-0619977.     

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.     

Exact and heuristic procedures for solving the fuzzy portfolio selection problem

We propose a fuzzy model for the portfolio selection problem which takes into account the vagueness of the investor’s preferences regarding the assumed risk. We also describe an exact method for solving it as well as a hybrid meta-heuristic procedure which is more adequate for medium and large-sized problems or in cases in which a quick solution is needed. As an application, we solve several problems based on data from the IBEX35 index and the Spanish Stock Exchange Interconnection System.     

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.     

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the ε-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.     

随机模糊的等比例-最小方差投资组合优化研究

Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。     

Fuzzy identification problem for continuous extremal fuzzy dynamic system

This work deals with the problems of the Continuous Extremal Fuzzy Dynamic System (CEFDS) optimization and briefly discusses the results developed by Sirbiladze (Int J Gen Syst 34(2):107–138, 2005a; 34(2):139–167, 2005b; 34(2):169–198, 2005c; 35(4):435–459, 2006a; 35(5):529–554, 2006b; 36(1): 19–58, 2007; New Math Nat Comput 4(1):41–60, 2008a; Mat Zametki, 83(3):439–460, 2008b). The basic properties of extended extremal fuzzy measures and Sugeno’s type integrals are considered and several variants of their representation are given. Values of extended extremal conditional fuzzy measures are defined as a levels of expert knowledge reflections of CEFDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed. A new approach in modeling of CEFDS is developed. Applying the results of Sirbiladze (Int J Gen Syst 34(2) 107–138, 2005a; 34(2):139–167, 2005b), fuzzy processes with possibilistic uncertainty, the source of which are expert knowledge reflections on the states on CEFDS in extremal fuzzy time intervals, are constructed (Sirbiladze in Int J Gen Syst 34(2):169–198, 2005c). The dynamics of CEFDS’s is described. Questions of the ergodicity of CEFDS are considered. A fuzzy-integral representation of a continuous extremal fuzzy process is given. Based on the fuzzy-integral model, a method and an algorithm are developed for identifying the transition operator of CEFDS. The CEFDS transition operator is restored by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states of CEFDS in the extremal fuzzy time intervals. The regularization condition for obtaining quasi-optimal estimator of the transition operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of CEFDS states.     

The possibilistic moments of fuzzy numbers and their applications

This paper, introduces the nearest weighted interval and point approximations of a fuzzy number, and then suggests weighted possibilistic moments about these points of fuzzy numbers. The possibilistic moments play an important role in fuzzy sets and systems, specifically in physics, mathematics and statistics. We provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory; some of their applications are mentioned.