Abstract
Tsallis entropy is a flexible extension of Shanon (logarithm) entropy. Since entropy measures indeterminacy of an uncertain random variable, this paper proposes the concept of partial Tsallis entropy for uncertain random variables as a flexible devise in chance theory. An approach for calculating partial Tsallis entropy for uncertain random variables, based on Monte Carlo simulation, is provided. As an application in finance, partial Tsallis entropy is invoked to optimize portfolio selection of uncertain random returns via crow search algorithm.
Highlights
In statistics, entropy measures the indeterminacy of a random variable
By inception of Shanon entropy for discrete random variables, Liu [12] presented the concept of entropy for uncertain variables
Ahmadzade et al [4] presented the concept of partial entropy for uncertain random variables and applied to portfolio selection problems via different models, for instance see [2, 3]. colorredIn this work, as an extension of logarithm entropy, we propose the flexible concept of Tsallis entropy and discuss about its properties
Summary
Entropy measures the indeterminacy of a random variable. Firstly, Shanon [22] proposed the concept of entropy of discrete random variables. Partial entropy of uncertain random variable ξ is defined as following. By inception of relation (1), we propose the concept of Tsallis entropy for uncertain random variables as follows: Definition 5 Let ξ be an uncertain random variable with chance distribution Φ(x). Partial Tsallis entropy of uncertain random variable ξ is defined as following. By invoking Theorem 3, we can write partial Tsallis entropy of an uncertain random variable via expectation of a function of random variables as follows:. In order to solve the portfolio selection problems with uncertain random returns, we propose two mean-variance-entropy models via partial Tsallis entropy. We want to optimize the portfolio selection problem via multi-objective model
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