scholarly journals Liu process and uncertain calculus

2013 ◽  
Vol 1 (1) ◽  
Author(s):  
Xiaowei Chen ◽  
Dan A Ralescu
Keyword(s):  
Liu Process ◽  
Uncertain Calculus

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.

A Rigorous Proof of Fundamental Theorem of Uncertain Calculus

2021 ◽  
pp. 2150009
Author(s):  
Tingqing Ye
Keyword(s):  
Fundamental Theorem ◽  
Rigorous Proof ◽  
Lipschitz Continuous ◽  
Sample Paths ◽  
Liu Process ◽  
Locally Lipschitz ◽  
Definition Of ◽  
Almost All ◽  
Uncertain Calculus ◽  
And Diffusion

This paper revises the definition of the general Liu process via requiring its drift and diffusion to be sample-continuous. Then it is verified that almost all sample paths of the general Liu process are locally Lipschitz continuous. At last, a rigorous proof of fundamental theorem of uncertain calculus is given.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

scholarly journals Fractional Liu process with application to finance

2009 ◽  
Vol 50 (9-10) ◽  
pp. 1538-1543 ◽  
Author(s):  
Zhongfeng Qin ◽  
Xin Gao
Keyword(s):  
Liu Process

scholarly journals Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

2021 ◽  
Vol 5 (3) ◽  
pp. 112
Author(s):  
Azmat Ullah Khan Niazi ◽  
Naveed Iqbal ◽  
Rasool Shah ◽  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon
Keyword(s):  
Differential Equations ◽  
Evolution Equations ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Exact Controllability ◽  
Fractional Evolution Equations ◽  
Liu Process ◽  
Bounded Space ◽  
Fractional Differential ◽  
Derivatives Of

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt with initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values from U(⊂EN),V(⊂EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations.

Uncertain Circuit Equation

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Yang Liu
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Time Domain ◽  
Electrical Circuit ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Liu Process ◽  
The Time Domain ◽  
Steady State Solutions ◽  
Transient And Steady State

Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.

Properties of Reflected Liu Process at the Origin

2014 ◽  
Vol 614 ◽  
pp. 421-424
Author(s):  
Cui Lian You ◽  
Xiao Yan Jiao
Keyword(s):  
Differential Equations ◽  
Liu Process ◽  
Fuzzy Process

Liu process is a special fuzzy process which plays an important role in the theory of fuzzy differential equations. This paper proposes the concept of reflected Liu process at the origin. Then some properties of this type of Liu process are deduced.

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