Sub mixed fractional Brownian motion and its application to finance

Ma, Pengcheng; Najafi, Alireza; Gomez-Aguilar, J.F.

doi:10.1016/j.chaos.2024.114968

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.114968

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Sub mixed fractional Brownian motion and its application to finance

Pengcheng Ma,

Alireza Najafi,

J.F. Gomez-Aguilar

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2024

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Cited by 3 publications

References 24 publications

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An efficient computational method for solving the fractional form of the European option price PDE with transaction cost under the fractional Heston model

Sawangtong,

Taghipour,

Najafi

2024

Engineering Analysis with Boundary Elements

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An efficient computational method for solving the fractional form of the European option price PDE with transaction cost under the fractional Heston model

Sawangtong,

Taghipour,

Najafi

2024

Engineering Analysis with Boundary Elements

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Global Mittag-Leffler Attractive Sets, Boundedness, and Finite-Time Stabilization in Novel Chaotic 4D Supply Chain Models with Fractional Order Form

Johansyah,

Sambas,

Farman

et al. 2024

Fractal Fract

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This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger maximal Lyapunov exponents (MLE) compared to the original model, indicating increased system complexity. The existence, uniqueness, and Ulam–Hyers stability of the proposed system are verified. Additionally, we establish the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the system. Numerical simulations and MATLAB phase portraits demonstrate the chaotic nature of the proposed system. Furthermore, a dynamical analysis achieves verification via the Lyapunov exponents, a bifurcation diagram, a 0–1 test, and a complexity analysis. A new numerical approximation method is proposed to solve non-linear fractional differential equations, utilizing fractional differentiation with a non-singular and non-local kernel. These numerical simulations illustrate the primary findings, showing that both external and internal factors can accelerate the process. Furthermore, a robust control scheme is designed to stabilize the system in finite time, effectively suppressing chaotic behaviors. The theoretical findings are supported by the numerical results, highlighting the effectiveness of the control strategy and its potential application in real-world supply chain management (SCM).

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The fractional soliton solutions: shaping future finances with innovative wave profiles in option pricing system

Rehman,

Wong,

Aljohani

et al. 2024

MATH

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<p>Financial engineering problems hold considerable significance in the academic realm, where there remains a continued demand for efficient methods to scrutinize and analyze these models. Within this investigation, we delved into a fractional nonlinear coupled system for option pricing and volatility. The model we examined can be conceptualized as a fractional nonlinear coupled wave alternative to the governing system of Black-Scholes option pricing. This introduced a leveraging effect, wherein stock volatility aligns with stock returns. To generate novel solitonic wave structures in the system, the present article introduced a generalized Ricatti mapping method and new Kudryashov method. Graphical representations, both in 3D and 2D formats, were employed to elucidate the system's response to pulse propagation. These visualizations enabled the anticipation of appropriate parameter values that align with the observed data. Furthermore, a comparative analysis of solutions was presented for different fractional order values. Additionally, the article showcases the comparison of wave profiles through 2D graphs. The results of this investigation suggested that the proposed method served as a highly reliable and flexible alternative for problem-solving, preserving the physical attributes inherent in realistic processes. To sum up, the main objective of our work was to conceptualize a fractional nonlinear coupled wave system as an alternative to the Black-Scholes option pricing model and investigate its implications on stock volatility and returns. Additionally, we aimed to apply and analyze methods for generating solitonic wave structures and compare their solutions for different fractional order values.</p>

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Sub mixed fractional Brownian motion and its application to finance

Cited by 3 publications

References 24 publications

An efficient computational method for solving the fractional form of the European option price PDE with transaction cost under the fractional Heston model

An efficient computational method for solving the fractional form of the European option price PDE with transaction cost under the fractional Heston model

Global Mittag-Leffler Attractive Sets, Boundedness, and Finite-Time Stabilization in Novel Chaotic 4D Supply Chain Models with Fractional Order Form

The fractional soliton solutions: shaping future finances with innovative wave profiles in option pricing system

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