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Parameter estimation of uncertain differential equation with application to financial market

Author

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  • Yang, Xiangfeng
  • Liu, Yuhan
  • Park, Gyei-Kark

Abstract

Uncertain differential equation (UDE) has been widely applied in the financial market, and many option pricing formulas are derived based on UDE. But the existing literature don’t consider the parameter estimation of UDE, and the parameters are just assumed as some given constants. This paper will present an approach to estimate the unknown parameter of UDE from discretely sampled data via α-path method for the first time. And the concepts of forecast value and confidence interval are introduced to predict the future value in a UDE. As five special UDEs, the parameters estimations of arithmetic Liu process, geometric Liu process, uncertain Ornstein-Uhlenbeck process, uncertain mean-reverting process, and uncertain exponential Ornstein-Uhlenbeck process are also derived, and the corresponding numerical examples are given. Furthermore, this paper proposes a means to estimate unknown parameters for the general geometric Liu process, and as an application, this method will be successfully used in Alibaba stock.

Suggested Citation

  • Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304240
    DOI: 10.1016/j.chaos.2020.110026
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Zhang, Zhiqiang & Liu, Weiqi & Sheng, Yuhong, 2016. "Valuation of power option for uncertain financial market," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 257-264.
    4. Yang, Xiangfeng & Zhang, Zhiqiang & Gao, Xin, 2019. "Asian-barrier option pricing formulas of uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 79-86.
    5. Zhang, Yi & Gao, Jinwu & Huang, Zhiyong, 2017. "Hamming method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 331-341.
    6. Lanruo Dai & Zongfei Fu & Zhiyong Huang, 2017. "Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 597-604, March.
    7. Banerjee, Amit & Abu-Mahfouz, Issam, 2014. "A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 65-83.
    8. Tian, Miao & Yang, Xiangfeng & Kar, Samarjit, 2019. "Equity warrants pricing problem of mean-reverting model in uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    9. Rakshit, Biswambhar & Chowdhury, A. Roy & Saha, Papri, 2007. "Parameter estimation of a delay dynamical system using synchronization in presence of noise," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1278-1284.
    10. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
    11. Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
    12. Tian, Miao & Yang, Xiangfeng & Zhang, Yi, 2019. "Barrier option pricing of mean-reverting stock model in uncertain environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 126-143.
    13. Wang, Xiao & Ning, Yufu & Moughal, Tauqir A. & Chen, Xiumei, 2015. "Adams–Simpson method for solving uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 209-219.
    14. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
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