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Fractional Liu uncertain differential equation and its application to finance

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  • Najafi, Alireza
  • Taleghani, Rahman

Abstract

This paper concentrates on fractional Liu as a long memory process to describe the uncertain part of the financial models. First, we study the existence and uniqueness solution of the fractional Liu differential equation by using the mathematical properties of the fractional Liu process. As well as applying statistical criteria, we indicate that the real data market has a long memory property. Then, we consider the fractional Liu geometric model and calibrate its parameters to predict the future asset price. Ultimately, we apply the Cardinality Constraints Mean–Variance (CCMV) and the proposed models to find portfolio optimization as a meaningful application of the fractional uncertain financial models.

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  • Najafi, Alireza & Taleghani, Rahman, 2022. "Fractional Liu uncertain differential equation and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010542
    DOI: 10.1016/j.chaos.2022.112875
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    1. Nathan Nunn, 2009. "The Importance of History for Economic Development," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 65-92, May.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    4. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    5. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    6. Duan Li & Xiaoling Sun & Jun Wang, 2006. "Optimal Lot Solution To Cardinality Constrained Mean–Variance Formulation For Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 83-101, January.
    7. Abhijit Banerjee & Lakshmi Iyer, 2005. "History, Institutions, and Economic Performance: The Legacy of Colonial Land Tenure Systems in India," American Economic Review, American Economic Association, vol. 95(4), pages 1190-1213, September.
    8. Sheng, Yuhong & Yao, Kai & Qin, Zhongfeng, 2020. "Continuity and variation analysis of fractional uncertain processes," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    11. 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).
    12. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    13. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    14. Shi, Gang & Gao, Jinwu, 2021. "European Option Pricing Problems with Fractional Uncertain Processes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    2. Li, Xiaoyan & Sun, Ni, 2023. "Comments for “Fractional Liu uncertain differential equation and its application to finance”," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Li, Bo & Tao, Ziyu & Shu, Yadong, 2025. "Uncertain Bass diffusion model and modeling the purchase volume of private cargo vehicles in China," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    4. Xin, Yue & Zhang, Yi & Noorani, Idin & Mehrdoust, Farshid & Gao, Jinwu, 2025. "Estimation of parameters and valuation of options written on multiple assets described by uncertain fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    5. Jiangong Wu & J. F. Gomez-Aguilar & Rahman Taleghani, 2025. "Portfolio Optimization Under the Uncertain Financial Model," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 571-592, July.
    6. Md. Habibur Rahman & Muhammad I. Bhatti & Nicholas Dimakis, 2025. "Solutions for Linear Fractional Differential Equations with Multiple Constraints Using Fractional B-Poly Bases," Mathematics, MDPI, vol. 13(19), pages 1-17, September.
    7. Wang, Huiwen & Li, Fang, 2025. "An operator method for composite fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).

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