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Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model

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  • Jin, Ting
  • Sun, Yun
  • Zhu, Yuanguo

Abstract

Uncertain fractional order differential equation is a significant tool for modeling the uncertain dynamic system. First, we consider solutions of an uncertain fractional order differential equation with the Caputo type and investigate inverse uncertain distributions of their time integral. On the basis of α-path, two different time integral theorems for inverse uncertain distributions are given. Second, in uncertain financial markets, the interest rate is considered as an uncertain process. As the application of the time integral, we present a novel zero-coupon bond model and derive a pricing formula of zero-coupon bond under this model. Last, by the predictor-corrector method, the numerical algorithm is designed. Analytic expressions and numerical calculations of the zero-coupon bond price are illustrated for fractional order mean-reverting model and standard deviation model, respectively.

Suggested Citation

  • Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s009630031930983x
    DOI: 10.1016/j.amc.2019.124991
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    Cited by:

    1. Jin, Ting & Ding, Hui & Xia, Hongxuan & Bao, Jinfeng, 2021. "Reliability index and Asian barrier option pricing formulas of the uncertain fractional first-hitting time model with Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
    3. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    4. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.

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