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THE SKEWNESS FOR uncertain random variable AND APPLICATION TO PORTFOLIO SELECTION PROBLEM

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第1期18卷 457-467页

作者： Li, Bo Shu, Yadong Nanjing Univ Finance & Econ Sch Appl Math Nanjing 210023 Peoples R China Nanjing Univ Informat Sci & Technol Sch Math & Stat Nanjing 210044 Peoples R China

uncertainty and randomness are two basic types of indeterminacy, where uncertain variable is used to represent quantities with human uncer-tainty and random variable is applied for modeling quantities with objective randomness. In many real systems, uncertainty and randomness often exist simultaneously. Then uncertain random variable and chance measure can be used to handle such cases. We know that the skewness is a measure of distri-butional asymmetry. However, the concept of skewness for uncertain random variable has not been clearly defined. In this paper, we first propose a con-cept of skewness for uncertain random variable and then present a formula for calculating the skewness via chance distribution. Applying the presented for-mula, the skewnesses of three special uncertain random variables are derived. Finally, a portfolio selection problem is carried out for showing the efficiency and applicability of skewness and presented formula.

关键词： randomness skewness uncertain random variable chance distribution uncertainty

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Evolutionary Multiobjective Optimization for Large-Scale Portfolio Selection With Both random and uncertain Returns

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第1期29卷 76-90页

作者： Liu, Weilong Zhang, Yong Liu, Kailong Quinn, Barry Yang, Xingyu Peng, Qiao Guangdong Univ Technol Sch Management Guangzhou 510520 Guangdong Peoples R China Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China Queens Univ Queens Business Sch Belfast BT9 5EE North Ireland Queens Univ Belfast Grp Informat Technol Analyt & Operat Belfast BT9 5EE North Ireland

With the advent of Big Data, managing large-scale portfolios of thousands of securities is one of the most challenging tasks in the asset management industry. This study uses an evolutionary multiobjective technique to solve large-scale portfolio optimization problems with both long-term listed and newly listed securities. The future returns of long-term listed securities are defined as random variables whose probability distributions are estimated based on sufficient historical data, while the returns of newly listed securities are defined as uncertain variables whose uncertainty distributions are estimated based on experts' knowledge. Our approach defines security returns as theoretically uncertain random variables and proposes a three-moment optimization model with practical trading constraints. In this study, a framework for applying arbitrary multiobjective evolutionary algorithms to portfolio optimization is established, and a novel evolutionary algorithm based on large-scale optimization techniques is developed to solve the proposed model. The experimental results show that the proposed algorithm outperforms state-of-the-art evolutionary algorithms in large-scale portfolio optimization.

关键词： Optimization Portfolios Security random variables uncertainty Evolutionary computation Mathematical models Evolutionary computations large-scale investment multiobjective optimization portfolio optimization uncertain random variable

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Negative cumulative extropy of uncertain variables with applications

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年第11期54卷 3135-3148页

作者： Tahmasebi, Saeid Ghimatgar, Hojat Ahmadzade, Hamed Persian Gulf Univ Fac Intelligent Syst Engn & Data Sci Dept Stat Bushehr Iran Persian Gulf Univ Fac Intelligent Syst Engn & Data Sci Dept Elect Engn Bushehr Iran Univ Sistan & Baluchestan Dept Stat Zahedan Iran

Recently, a measure of uncertainty termed by negative cumulative extropy (NCEX) is proposed by Tahmasebi and Toomaj (2022). It is a flexible extension of extropy measure which was proposed by Lad, Sanfilippo, and Agro (2015). To measure the uncertainty of uncertain variables, in this article, we propose the concept of NCEX through uncertainty distributions. Some properties of NCEX are derived, and some practical examples of uncertain variables are given. Several basic theorems are proposed. A formula of cross-extropy is defined via inverse uncertainty distributions. We also delve into a pattern recognition problem to highlight the importance of cross-extropy. Finally, applications to portfolio selection and signal processing are presented.

关键词： Chance theory extropy measure uncertain random variable negative cumulative extropy pattern recognition

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OPTIMAL CONTROL PROBLEMS OF MULTI-STAGE uncertain random SYSTEMS BASED ON CHANCE MEASURE

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2025年第5期21卷 4184-4205页

作者： Xu, Qinqin Zhu, Yuanguo Nanjing Univ Posts & Telecommun Sch Sci Nanjing 210023 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Math & Stat Nanjing 210094 Jiangsu Peoples R China

Chance measure is widely considered to be a fundamental mathematical characteristic of uncertain random systems, which exhibit both objective randomness and subjective uncertainty simultaneously. Serving as an indicator of belief degree, it quantifies the likelihood of uncertain random events. This paper focuses on the optimal control problem for multi-stage uncertain random systems using chance measures. Firstly, we establish an optimal control model for uncertain random systems and provide the corresponding equivalent forms and recursive equations. Next, the analytical solutions for the optimal controls and optimal values of two specific problems are derived. For the general optimal control problem, we propose an online optimization method based on a hybrid intelligent algorithm. Finally, an optimal scheduling strategy applying recent water resources data of China is developed satisfying the multi-stage uncertain random optimal control problems.

关键词： uncertain random variable multi-stage system optimal control chance measure recurrence equation

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uncertain random variables and laws of large numbers under U-C chance space

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FUZZY SETS AND SYSTEMS 2024年 493卷

作者： Hu, Feng Fu, Xiaoting Qu, Ziyi Qufu Normal Univ Sch Stat & Data Sci Qufu 273165 Peoples R China

uncertainty theory was founded by Baoding Liu for modeling belief degrees about human uncertainty. And chance theory was pioneered by Yuhan Liu based on probability theory and uncertainty theory. In many cases, imprecise risk situation in subjective or objective setting and human uncertainty simultaneously appear in a complex system. To measure uncertain random events in this system, this paper combines uncertainty space with convex non-additive probability space into a new kind of two-dimensional chance space called U-C chance space. Moreover, a new framework for uncertain random variables combining uncertainty theory with convex non- additive probability theory is provided. For applications of this new framework, it can be applied to characterize some kinds of phenomena which possess the characteristics of both imprecise risk situations and belief degrees about human uncertainty in situations of great events, such as financial crisis, major natural disaster, etc. The main contribution of this paper is to derive the types of Kolmogorov and Marcinkiewicz-Zygmund LLNs for uncertain random variables satisfying some conditions under U-C chance space, where the convex non-additive probability is totally monotone. Furthermore, several examples are stated and explained.

关键词： uncertain random variable Convex non-additive probability U-C chance theory Law of large numbers

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uncertain random variables: a mixture of uncertainty and randomness

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SOFT COMPUTING 2013年第4期17卷 625-634页

作者： Liu, Yuhan Tsinghua Univ Dept Ind Engn Beijing 100084 Peoples R China

In many cases, human uncertainty and objective randomness simultaneously appear in a system. In order to describe this phenomena, this paper presents a new concept of uncertain random variable. To measure uncertain random events, this paper also combines probability measure and uncertain measure into a chance measure. Based on the tool of chance measure, the concepts of chance distribution, expected value and variance of uncertain random variable are proposed.

关键词： uncertainty theory Probability theory uncertain random variable Chance measure

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Law of large numbers for uncertain random variables with different chance distributions

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2016年第3期31卷 1227-1234页

作者： Gao, Rong Sheng, Yuhong Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China Xinjiang Univ Coll Math & Syst Sci Urumqi Peoples R China

Chance theory is put forward as a tool to deal with a complex system including randomness and uncertainty. As a fundamental concept in chance theory, uncertain random variable is an extension of random variable and uncertain variable. This paper obtains a new law of large numbers for independent uncertain random variables but not necessarily identically distributed.

关键词： uncertain variable uncertain random variable law of large numbers

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Complex uncertain random variables

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SOFT COMPUTING 2018年第17期22卷 5817-5824页

作者： Gao, Rong Zhang, Zhiqiang Ahmadazde, Hamed Ralescu, Dan A. Hebei Univ Technol Sch Econ & Management Tianjin 300401 Peoples R China Shanxi Datong Univ Sch Math & Comp Sci Datong 037009 Peoples R China Univ Sistan & Baluchestan Dept Stat Zahedan Iran Univ Cincinnati Dept Math Sci Cincinnati OH 45221 USA

One can identify at least two types of inexactness: one is randomness associated with frequencies and the other is uncertainty associated with belief degrees. However, randomness and uncertainty usually exist in a complex system simultaneously. To model such complex phenomena, we present a concept of complex uncertain random variable. Then, we derive the complex chance distributions of complex uncertain random variables. Moreover, the expected value and variance of a complex uncertain random variable are also studied. Finally, we define and study the complex linear and normal uncertain random variables.

关键词： uncertainty theory uncertain variable uncertain random variable Chance distribution Complex variable

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A new definition of cross entropy for uncertain random variables and its application

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018年第1期35卷 1193-1204页

作者： Jia, Lifen Yang, Xiangfeng Gao, Xin Tsinghua Univ Dept Math Sci Beijing Peoples R China Univ Int Business & Econ Sch Informat Technol & Management Beijing Peoples R China North China Elect Power Univ Sch Math Sci & Phys Beijing 102206 Peoples R China

This paper proposes a new definition of cross entropy for uncertain random variables, and derives a formula. Moreover, this paper introduces generalized cross entropy for uncertain random variables, and discusses its properties. Based on the definition of cross entropy, a cross entropy chance distribution model of degree-constrained minimum spanning tree (DCMST) problem is proposed. An algorithm is designed here to solve the model. Finally, a numerical example is provided to illustrate the effectiveness of the proposed model and algorithm.

关键词： Cross entropy uncertain random variable minimum spanning tree uncertain random network

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Elliptic entropy of uncertain random variables with application to portfolio selection

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SOFT COMPUTING 2021年第3期25卷 1925-1939页

作者： Chen, Lin Gao, Rong Bian, Yuxiang Di, Huafei Tianjin Univ Coll Management & Econ Tianjin 300072 Peoples R China Hebei Univ Technol Sch Econ & Management Tianjin 300401 Peoples R China East China Univ Polit Sci & Law Sch Business Shanghai 201620 Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China

This paper investigates an elliptic entropy of uncertain random variables and its application in the area of portfolio selection. We first define the elliptic entropy to characterize the uncertainty of uncertain random variables and give some mathematical properties of the elliptic entropy. Then we derive a computational formula to calculate the elliptic entropy of function of uncertain random variables. Furthermore, we use the elliptic entropy to characterize the risk of investment and establish a mean-entropy portfolio selection model, in which the future security returns are described by uncertain random variables. Based on the chance theory, the equivalent form of the mean-entropy model is derived. To show the performance of the mean-entropy portfolio selection model, several numerical experiments are presented. We also numerically compare the mean-entropy model with the mean-variance model, the equi-weighted portfolio model, and the most diversified portfolio model by using three kinds of diversification indices. Numerical results show that the mean-entropy model outperforms the mean-variance model in selecting diversified portfolios no matter of using which diversification index.

关键词： uncertainty theory Elliptic entropy uncertain random variable Chance theory Mean-entropy model Diversification index

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