# American Institute of Mathematical Sciences

• Previous Article
A stochastic model and social optimization of a blockchain system based on a general limited batch service queue
• JIMO Home
• This Issue
• Next Article
On limiting characteristics for a non-stationary two-processor heterogeneous system with catastrophes, server failures and repairs
doi: 10.3934/jimo.2020163

## The skewness for uncertain random variable and application to portfolio selection problem

 1 School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China 2 School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

* Corresponding author: Bo Li

Received  June 2020 Revised  August 2020 Published  November 2020

Uncertainty and randomness are two basic types of indeterminacy, where uncertain variable is used to represent quantities with human uncertainty 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 distributional asymmetry. However, the concept of skewness for uncertain random variable has not been clearly defined. In this paper, we first propose a concept of skewness for uncertain random variable and then present a formula for calculating the skewness via chance distribution. Applying the presented formula, 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.

Citation: Bo Li, Yadong Shu. The skewness for uncertain random variable and application to portfolio selection problem. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020163
##### References:

show all references

##### References:
The computational results for different $p$ and $q$
 $(p, q)$ $(x_{1}^{*}, x_{2}^{*})$ Expected value Variance Skewness $(0.04, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.04, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.04, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$
 $(p, q)$ $(x_{1}^{*}, x_{2}^{*})$ Expected value Variance Skewness $(0.04, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.04, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.04, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.02, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.2)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.5)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$ $(0.01, 0.8)$ $(0, 1)$ $0.04$ 0.0075 $1.125\times10^{-4}$
 [1] Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020164 [2] Shiqi Ma. On recent progress of single-realization recoveries of random Schrödinger systems. Electronic Research Archive, , () : -. doi: 10.3934/era.2020121 [3] Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 [4] Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011 [5] Yangrong Li, Shuang Yang, Qiangheng Zhang. Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation. Electronic Research Archive, 2020, 28 (4) : 1529-1544. doi: 10.3934/era.2020080 [6] Yongge Tian, Pengyang Xie. Simultaneous optimal predictions under two seemingly unrelated linear random-effects models. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020168

2019 Impact Factor: 1.366

## Tools

Article outline

Figures and Tables