Uncertain production risk process with breakdowns and its shortage index and shortage time

2020 ◽  
Vol 39 (5) ◽  
pp. 7151-7160
Author(s):  
Waichon Lio ◽  
Lifen Jia
Keyword(s):  
Uncertainty Theory ◽  
Risk Process ◽  
Uncertainty Distribution ◽  
Production Risk ◽  
Numerical Examples ◽  
Cycle Times ◽  
Production Problem

Since the practical production is not continuously available and sometimes suffers unexpected breakdowns, this paper applies uncertainty theory to introducing an uncertain production risk process with breakdowns to handle the production problem with uncertain cycle times (consisting of uncertain on-times and uncertain off-times) and uncertain production amounts. The concept of shortage index of the uncertain production risk process with breakdowns is provided and some formulas for the calculation are given. Furthermore, the shortage time of the uncertain production risk process with breakdowns is proposed and its uncertainty distribution is obtained. Finally, some numerical examples are revealed.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

Shortage Index and Shortage Time of Uncertain Production Risk Process

2020 ◽  
Vol 28 (11) ◽  
pp. 2856-2863 ◽  
Author(s):  
Waichon Lio ◽  
Baoding Liu
Keyword(s):  
Risk Process ◽  
Production Risk

A new measure of indeterminacy for uncertain variables with application to portfolio selection

2021 ◽  
pp. 1-5
Author(s):  
Jin Liu ◽  
Jinsheng Xie ◽  
Hamed Ahmadzade ◽  
Mehran Farahikia
Keyword(s):  
Probability Theory ◽  
Portfolio Selection ◽  
Uncertainty Theory ◽  
Random Variable ◽  
Uncertain Variable ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Selection Problems ◽  
Exponential Entropy

Entropy is a measure for characterizing indeterminacy of a random variable or an uncertain variable with respect to probability theory and uncertainty theory, respectively. In order to characterize indeterminacy of uncertain variables, the concept of exponential entropy for uncertain variables is proposed. For computing the exponential entropy for uncertain variables, a formula is derived via inverse uncertainty distribution. As an application of exponential entropy, portfolio selection problems for uncertain returns are optimized via exponential entropy-mean models. For better understanding, several examples are provided.

scholarly journals A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2429
Author(s):  
Yuxing Jia ◽  
Yuer Lv ◽  
Zhigang Wang
Keyword(s):  
Uncertainty Theory ◽  
Monotone Function ◽  
Uncertain Variable ◽  
Mathematical Tool ◽  
Human Beings ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
New Ideas ◽  
New Formula ◽  
Theory Uncertainty

As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.

scholarly journals An Uncertain Alternating Renewal Insurance Risk Model

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Zhai ◽  
Haitao Zheng ◽  
Manying Bai ◽  
Yunyun Jiang
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Risk ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Ruin Time ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Explicit Expressions ◽  
Insurance Risk Model

The claim process in an insurance risk model with uncertainty is traditionally described by an uncertain renewal reward process. However, the claim process actually includes two processes, which are called the report process and the payment process, respectively. An alternative way is to describe the claim process by an uncertain alternating renewal reward process. Therefore, this paper proposes an insurance risk model under uncertain measure in which the claim process is supposed to be an alternating renewal reward process and the premium process is regarded as a renewal reward process. Then, the paper also gives the inverse uncertainty distribution of the insurance risk process. The expression of ruin index and the uncertainty distribution of the ruin time are derived which both have explicit expressions based on given uncertainty distributions. Finally, several examples are provided to illustrate the modeling ideas.

A Stock Model with Varying Stock Diffusion for Uncertain Market

2018 ◽  
Vol 26 (04) ◽  
pp. 679-692
Author(s):  
Shengguo Li ◽  
Jin Peng ◽  
Bo Zhang
Keyword(s):  
Option Pricing ◽  
Uncertainty Theory ◽  
European Option ◽  
Numerical Examples ◽  
European Option Pricing ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Stock Model

The option-pricing problem is an important topic in modern finance. In this paper, we propose a stock model with varying stock diffusion based on uncertainty theory. The European option pricing formulas are derived from the proposed uncertain stock model, and some mathematical properties of these formulas are investigated. Moreover, extended uncertain stock models are introduced and discussed. Finally, numerical examples are given to illustrate the proposed model.

SOME PROPERTIES OF CONTINUOUS UNCERTAIN MEASURE

2009 ◽  
Vol 17 (03) ◽  
pp. 419-426 ◽  
Author(s):  
XIN GAO
Keyword(s):  
Uncertainty Theory ◽  
Uncertain Variable ◽  
Expected Value ◽  
Critical Values ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Convergence Theorems ◽  
Basic Properties

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

RECURSIVE CALCULATION OF RUIN PROBABILITIES AT OR BEFORE CLAIM INSTANTS FOR NON-IDENTICALLY DISTRIBUTED CLAIMS

2014 ◽  
Vol 45 (2) ◽  
pp. 421-443 ◽  
Author(s):  
Anisoara Maria Raducan ◽  
Raluca Vernic ◽  
Gheorghita Zbaganu
Keyword(s):  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Recursive Algorithm ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Claim Number ◽  
Recursive Calculation ◽  
The Impact

AbstractIn this paper, we present recursive formulae for the ruin probability at or before a certain claim arrival instant for some particular continuous time risk model. The claim number process underlying this risk model is a renewal process with either Erlang or a mixture of exponentials inter-claim times (ICTs). The claim sizes (CSs) are independent and distributed in Erlang's family, i.e., they can have different parameters, which yields a non-homogeneous risk process. We present the corresponding recursive algorithm used to evaluate the above mentioned ruin probability and we illustrate it on several numerical examples in which we vary the model's parameters to assess the impact of the non-homogeneity on the resulting ruin probability.

Complex uncertain differential equations with application to time integral

2021 ◽  
pp. 1-15
Author(s):  
Zhifu Jia ◽  
Xinsheng Liu
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Uncertainty Theory ◽  
Numerical Algorithms ◽  
Existence And Uniqueness Theorem ◽  
Uncertainty Distribution ◽  
Time Integral ◽  
Liu Process ◽  
Homogeneous Linear

In this paper, we propose complex uncertain differential equations (CUDEs) based on uncertainty theory. In order to describe the evolution of complex uncertain phenomenon related to belief degrees, we apply the complex Liu process to CUDEs. Firstly, we pose a concept of a linear CUDE and prove that homogeneous linear CUDE and general linear CUDE have solutions. Then, we prove existence and uniqueness theorem of a special CUDE. Further, we design a numerical algorithm to obtain inverse uncertainty distribution of the solution. Finally, as an application, we analyse the inverse uncertainty distributions of time integral of CUDEs and design numerical algorithms to obtain inverse uncertainty distributions of time integral.

Uncertain Statistics and COVID-19 Spread in China

2021 ◽  
pp. 2150008
Author(s):  
Waichon Lio
Keyword(s):  
Differential Equation ◽  
Regression Analysis ◽  
Uncertainty Theory ◽  
Hypothesis Test ◽  
Uncertain Differential Equation ◽  
Uncertainty Distribution ◽  
Times Series ◽  
Mathematical Techniques ◽  
Uncertain Statistics ◽  
Estimation Of Uncertainty

Uncertain statistics is a set of mathematical techniques for collecting, analyzing and interpreting data by uncertainty theory. In this paper, the main topics of uncertain statistics, including estimation of uncertainty distribution, uncertain regression analysis, uncertain times series, uncertain differential equation and uncertain hypothesis test, are reviewed. Furthermore, by the application to the COVID-19 spread in China, the advantages of those techniques in uncertain statistics are sorted out.

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