Some applications of possibilistic mean value, variance, covariance and correlation

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as wel

How to Handle Uncertainty

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On-Line Portfolio Selection Strategy Based on Weighted Moving Average Asymmetric Mean Reversion

Mean reversion is an important property for constructing efficient on-line portfolio selection strategy. The existing strategies mostly suppose that the mean reversion is multi-period symmetric or single-period asymmetric. However, the mean reversion is multi-period and asymmetric in the real market. Taking this into account, on-line strategies based on multi-period asymmetric mean reversion is proposed. With designing multi-piecewise loss function and imitating passive aggressive algorithm, we propose a new on-line strategy WMAAMR. This strategy runs in linear time, and thus is suitable for large-scale trading applications. Empirical results on four real markets show that WMAAMR can achieve better results and bear higher transaction cost rate

Dynamic changes and multi-dimensional evolution of portfolio optimization

Although there has been an increasing number of studies investigate portfolio optimization from different perspectives, few attempts could be found that focus on the development trend and hotspots of this research area. Therefore, it motivates us to comprehensively investigate the development of portfolio optimization research and give some deep insights into this knowledge domain. In this paper, some bibliometric methods are utilized to analyse the status quo and emerging trends of portfolio optimization research on various aspects such as authors, countries and journals. Besides, ‘theories’, ‘models’ and ‘algorithms’, especially heuristic algorithms are identified as the hotspots in the given periods. Furthermore, the evolutionary analysis tends to presents the dynamic changes of the cutting-edge concepts of this research area in the time dimension. It is found that more portfolio optimization studies were at an exploration stage from mean-variance analysis to consideration of multiple constraints. However, heuristic algorithms have become the driving force of portfolio optimization research in recent years. Multidisciplinary analyses and applications are also the main trends of portfolio optimization research. By analysing the dynamic changes and multi-dimensional evolution in recent decades, we contribute to presenting some deep insights of the portfolio optimization research directly, which assists researchers especially beginners to comprehensively learn this research field

A FUZZY BI-LEVEL PROJECT PORTFOLIO PLANNING CONSIDERING THE DECENTRALIZED STRUCTURE OF PHARMACY HOLDINGS

Research and development (R&D) in the pharmaceutical industry requires proper and optimal planning and management because of its critical role in public health. Taking into account a decentralized decision-making structure in R&D management in pharmaceutical holding companies, this study introduces a new fuzzy bi-level multi-follower mathematical optimization model to address budget allocation and project portfolio planning. Specifically, the holding company's head office, as the leader, and the subsidiaries, as followers, make strategic and operational decisions concerning important issues such as budget allocation and portfolio selection and scheduling. Since the lower level represents multiple mixed-integer programming problems with uncooperative reference relationships between followers, solving the resulting bi-level model is challenging. Therefore, our model is based on an effective hybrid solution methodology, which converts the bi-level model, including multiple followers, into a single-level model. In order to validate the proposed model, we conducted a case study and analyzed the strategies of each actor within the conglomerate. Based on the results of experiments, it is evident that a strategy that focuses on one level of operations profoundly affects decisions at the other level

Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments

Forecasting Cryptocurrency Value by Sentiment Analysis: An HPC-Oriented Survey of the State-of-the-Art in the Cloud Era

This chapter surveys the state-of-the-art in forecasting cryptocurrency value by Sentiment Analysis. Key compounding perspectives of current challenges are addressed, including blockchains, data collection, annotation, and filtering, and sentiment analysis metrics using data streams and cloud platforms. We have explored the domain based on this problem-solving metric perspective, i.e., as technical analysis, forecasting, and estimation using a standardized ledger-based technology. The envisioned tools based on forecasting are then suggested, i.e., ranking Initial Coin Offering (ICO) values for incoming cryptocurrencies, trading strategies employing the new Sentiment Analysis metrics, and risk aversion in cryptocurrencies trading through a multi-objective portfolio selection. Our perspective is rationalized on the perspective on elastic demand of computational resources for cloud infrastructures

A framework of distributionally robust possibilistic optimization

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in scenario set, which in turn describes an ambiguity set of probability distributions in scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust and expected value approaches, commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified