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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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    3. Li, Xiaoyan & Sun, Ni, 2023. "Comments for “Fractional Liu uncertain differential equation and its application to finance”," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Xiangfeng Yang & Haoxuan Li, 2025. "Uncertain finance: a systematic review of recent advances," Fuzzy Optimization and Decision Making, Springer, vol. 24(3), pages 531-561, September.
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    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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