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.     

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.     

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 risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments

Due to changes of situation in financial markets and investors’ preferences towards risk, an existing portfolio may not be efficient after a period of time. In this paper, we propose a possibilistic risk tolerance model for the portfolio adjusting problem based on possibility moments theory. A Sequential Minimal Optimization (SMO)-type decomposition method is developed for finding exact optimal portfolio policy without extra matrix storage. We present a simple method to estimate the possibility distributions for the returns of assets. A numerical example is provided to illustrate the effectiveness of the proposed models and approaches.     

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.     

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.     

Possibilistic nested logic programs and strong equivalence

In this paper, the class of possibilistic nested logic programs is introduced. These possibilistic logic programs allow us to use nested expressions in the bodies and heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibilistic logic is defined. In order to define a general method for computing the possibilistic answer sets of a possibilistic nested program, the idea of equivalence between possibilistic nested programs is explored. By considering properties of equivalence between possibilistic programs, a process of transforming a possibilistic nested logic program into a possibilistic disjunctive logic program is defined. Given that our approach is an extension of answer set programming, we also explore the concept of strong equivalence between possibilistic nested logic programs. To this end, we introduce the concept of poss SE-models. Therefore, we show that two possibilistic nested logic programs are strong equivalents whenever they have the same poss SE-models.The expressiveness of the possibilistic nested logic programs is illustrated by a scenario from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded by vagueness and qualitative information.     

Weighted portfolio selection models based on possibility theory

In this paper, we discuss portfolio selection problem in a fuzzy uncertain environment. Based on the Fullér’s and Zhang’s notations, we discuss some properties of weighted lower and upper possibilistic means and variances as in probability theory. We further present two weighted possibilistic portfolio selection models with bounded constraint, which can be transformed to linear programming problems under the assumption that the returns of assets are trapezoidal fuzzy numbers. At last, a numerical example is given to illustrate our proposed effective means and approaches.     

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.     

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.     

Relating and extending semantical approaches to possibilistic reasoning

Two main semantical approaches to possibilistic reasoning with classical propositions have been proposed in the literature. Namely, Dubois-Prade's approach known as possibilistic logic, whose semantics is based on a preference ordering in the set of possible worlds, and Ruspini's approach that we redefine and call similarity logic, which relies on the notion of similarity or resemblance between worlds. In this article we put into relation both approaches, and it is shown that the monotonic fragment of possibilistic logic can be semantically embedded into similarity logic. Furthermore, to extend possibilistic reasoning to deal with fuzzy propositions, a semantical reasoning framework, called fuzzy truth-valued logic, is also introduced and proved to capture the semantics of both possibilistic and similarity logics.     

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.     

Using possibilistic logic for modeling qualitative decision: Answer Set Programming algorithms

A qualitative approach to decision making under uncertainty has been proposed in the setting of possibility theory, which is based on the assumption that levels of certainty and levels of priority (for expressing preferences) are commensurate. In this setting, pessimistic and optimistic decision criteria have been formally justified. This approach has been transposed into possibilistic logic in which the available knowledge is described by formulas which are more or less certainly true and the goals are described in a separate prioritized base. This paper adapts the possibilistic logic handling of qualitative decision making under uncertainty in the Answer Set Programming (ASP) setting. We show how weighted beliefs and prioritized preferences belonging to two separate knowledge bases can be handled in ASP by modeling qualitative decision making in terms of abductive logic programming where (uncertain) knowledge about the world and prioritized preferences are encoded as possibilistic definite logic programs and possibilistic literals respectively. We provide ASP-based and possibilistic ASP-based algorithms for calculating optimal decisions and utility values according to the possibilistic decision criteria. We describe a prototype implementing the algorithms proposed on top of different ASP solvers and we discuss the complexity of the different implementations.     

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.     

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.     

A note on the convexity assumption of possibilistic correlation

In 2005, Carlsson, Fullér and Majlender introduced a measure of possibilistic correlation of fuzzy numbers A and B by their joint possibility distributionC as an average degree of interaction between the γ-level sets of A and B as compared to their individual dispersions. They proved that this possibilistic correlation coefficient can never exceed 1 in absolute value, if all γ-level sets of the joint possibility distribution C are convex.In this communication, we shall formulate a special class of joint possibility distributions with non-convex γ-level sets, for which the correlation coefficient can take values outside the interval [−1,1]. In particular, this result will show that the assumption about the convexity of the level sets of C is essential for the possibilistic correlation to be bounded by the interval [−1,1].     

Portfolio selection with a new definition of risk

In the field of portfolio selection, variance, semivariance and probability of an adverse outcome are three best-known mathematical definitions of risk. Lots of models were built to minimize risk based on these definitions. This paper gives a new definition of risk for portfolio selection and proposes a new type of model based on this definition. In addition, a hybrid intelligent algorithm is employed to solve the optimization problem in general cases. One numerical example is also presented for the sake of illustration.     

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.     

On the impact of conditional expectation estimators in portfolio theory

In this paper, we investigate the implications for portfolio theory of using conditional expectation estimators. First, we focus on the approximation of the conditional expectation within large-scale portfolio selection problems. In this context, we propose a new consistent multivariate kernel estimator to approximate the conditional expectation and it optimizes the bandwidth selection of kernel-type estimators. Second, we deal with the portfolio selection problem from the point of view of different non-satiable investors, namely risk-averse and risk-seeker investors. In particular, using a well-known ordering classification, we first identify different definitions of returns based on the investors preferences. Finally, for each problem, we examine several admissible portfolio optimization problems applied to the US stock market. The proposed empirical analysis allows us to evaluate the impact of the conditional expectation estimators in portfolio theory.     

Lukasiewicz-based merging possibilistic networks

Possibility theory provides a good framework for dealing with merging problems when information is pervaded with uncertainty and inconsistency. Many merging operators in possibility theory have been proposed. This paper develops a new approach to merging uncertain information modeled by possibilistic networks. In this approach we restrict our attention to show how a “triangular norm” establishes a lower bound on the degree to which an assessment is true when it is obtained by a set of initial hypothesis represented by a joint possibility distribution. This operator is characterized by its high effect of reinforcement. A strongly conjunctive operator is suitable to merge networks that are not involved in conflict, especially those supported by both sources. In this paper, the Lukasiewicz t-norm is first applied to a set of possibility measures to combine networks having the same and different graphical structures. We then present a method to merge possibilistic networks dealing with cycles.