Uncertainty Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 905

Special Issue Editors


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Guest Editor
School of Economics and Management, North China Electric Power University, Beijing 102206, China
Interests: uncertainty theory; uncertain differential equations; reliability

Special Issue Information

Dear Colleagues,

Something is called random if its frequency of occurrence is known. Otherwise, it is called uncertain. In order to rationally deal with these phenomena, there exist two mathematical systems: probability theory and uncertainty theory. Probability theory is a branch of mathematics concerned with the analysis of random phenomena, while uncertainty theory is a branch of mathematics concerned with the analysis of uncertain phenomena. In order to use them to handle some quantity (e.g., stock price) in practice, the first action is to produce a distribution function representing the possibility that the quantity falls on the left side of the current point. If you believe the distribution function is close enough to the future frequency, then you should use probability theory. Otherwise, you have to use uncertainty theory. Numerous empirical studies show that the real world is far from frequency stable. This fact makes the distribution function obtained in practice usually deviate from the future frequency even when numerous observed data are available, which consequently provides motivation to learn and use uncertainty theory. This Special Issue explores the practical uses of uncertainty theory in fields like finance, engineering, and healthcare. It shows how uncertainty can be quantified and integrated into statistical models to enhance the accuracy and reliability of predictions and decisions.

Moreover, this Special Issue presents case studies and examples to demonstrate how uncertainty theory can be implemented to solve complex problems in real-world scenarios. This Special Issue welcomes all submissions related to uncertainty theory and applications.

Dr. Zhe Liu
Dr. Hua Ke
Guest Editors

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Keywords

  • uncertainty theory
  • uncertain differential equations
  • reliability
  • fuzzy logic
  • Bayesian statistics
  • decision-making
  • multi-agent
  • uncertainty theory
  • uncertain dynamic systems
  • uncertain statistics
  • uncertain programming
  • uncertain logic
  • uncertain differential equation
  • uncertain inference

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Published Papers (1 paper)

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Research

19 pages, 1581 KiB  
Article
A Structural Credit Risk Model with Jumps Based on Uncertainty Theory
by Hong Huang, Meihua Jiang, Yufu Ning and Shuai Wang
Mathematics 2025, 13(6), 897; https://doi.org/10.3390/math13060897 - 7 Mar 2025
Viewed by 552
Abstract
This study, within the framework of uncertainty theory, employs an uncertain differential equation with jumps to model the asset value process of a company, establishing a structured model of uncertain credit risk that incorporates jumps. This model is applied to the pricing of [...] Read more.
This study, within the framework of uncertainty theory, employs an uncertain differential equation with jumps to model the asset value process of a company, establishing a structured model of uncertain credit risk that incorporates jumps. This model is applied to the pricing of two types of credit derivatives, yielding pricing formulas for corporate zero-coupon bonds and Credit Default Swap (CDS). Through numerical analysis, we examine the impact of asset value volatility and jump magnitude on corporate default uncertainty, as well as the influence of jump magnitude on the pricing of zero-coupon bonds and CDS. The results indicate that an increase in volatility levels significantly enhances default uncertainty, and an expansion in the magnitude of negative jumps not only directly elevates default risk but also leads to a significant increase in the value of zero-coupon bonds and the price of CDS through a risk premium adjustment mechanism. Therefore, when assessing corporate default risk and pricing credit derivatives, the disturbance of asset value jumps must be considered a crucial factor. Full article
(This article belongs to the Special Issue Uncertainty Theory and Applications)
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