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On the mixed fractional Brownian motion

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  • Mounir Zili

Abstract

The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the α -differentiability of its sample paths.

Suggested Citation

  • Mounir Zili, 2006. "On the mixed fractional Brownian motion," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-9, August.
    • Handle: RePEc:hin:jnijsa:032435
    DOI: 10.1155/JAMSA/2006/32435
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    Cited by:

    1. Arthur Yosef, 2021. "Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1366-1381, September.
    2. Djeutcha, Eric & Kamdem, Jules Sadefo, 2021. "Local and implied volatilities with the mixed-modified-fractional-Dupire model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    4. Eric Djeutcha & Jules Sadefo-Kamdem & Louis Aimé Fono, 2021. "Mixed Modified Fractional Merton model of the bear spread Basket put option using the multidimensional Mellin transform," Working Papers hal-03330043, HAL.
    5. Wei-Guo Zhang & Zhe Li & Yong-Jun Liu & Yue Zhang, 2021. "Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 483-515, August.
    6. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    7. Alexander Kukush & Stanislav Lohvinenko & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 159-187, April.
    8. Axel A. Araneda, 2019. "The fractional and mixed-fractional CEV model," Papers 1903.05747, arXiv.org, revised Jun 2019.
    9. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, June.

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