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Alishahi, Marziyeh, Yarahmadi, Majid. (1405). New optimal adaptive stepsize algorithm for solving black-scholes equation. سامانه مدیریت نشریات علمی, 14(2), 633-651. doi: 10.22034/cmde.2025.65090.2974
Marziyeh Alishahi; Majid Yarahmadi. "New optimal adaptive stepsize algorithm for solving black-scholes equation". سامانه مدیریت نشریات علمی, 14, 2, 1405, 633-651. doi: 10.22034/cmde.2025.65090.2974
Alishahi, Marziyeh, Yarahmadi, Majid. (1405). 'New optimal adaptive stepsize algorithm for solving black-scholes equation', سامانه مدیریت نشریات علمی, 14(2), pp. 633-651. doi: 10.22034/cmde.2025.65090.2974
Alishahi, Marziyeh, Yarahmadi, Majid. New optimal adaptive stepsize algorithm for solving black-scholes equation. سامانه مدیریت نشریات علمی, 1405; 14(2): 633-651. doi: 10.22034/cmde.2025.65090.2974

New optimal adaptive stepsize algorithm for solving black-scholes equation

Computational Methods for Differential Equations
مقاله 9، دوره 14، شماره 2، تیر 2026، صفحه 633-651    اصل مقاله (12.92 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65090.2974
نویسندگان
Marziyeh Alishahi؛ Majid Yarahmadi*
Department of Mathematics and Computer Science, Lorestan University, Khorramabad, Lorestan 44316-68151, Iran.
چکیده
In this paper, a new algorithm is designed based on a state feedback global error control system, Laplace trans form, order reduction method, and k-step numerical integration methods to numerically solve the Black-Scholes equation. For this purpose, the Black-Scholes equation is converted into a first-order system of ordinary differ ential equations by using the Laplace transform and order reduction method. Also, a new robust linear optimal adaptive global error control dynamic for designing an adaptive time variant step size sequence is modeled and a corresponding optimal control law based on robust and optimal eigenvalue assignment is designed. The proposed optimal control law guarantees the absolute stability of the implemented k-step numerical integrator methods.  Finally, the transformed approximate solution of the Black-Scholes equation has been obtained using the Stefhest inverse Laplace transformation algorithm. The simulation examples show that the optimal control of global error under a given tolerance level, the guarantee of absolute stability, and the best approximation of sensitivity analysis indexes for the proposed approximate solution of the Black-Scholes equation is among the important advantages of the proposed method.
کلیدواژه‌ها
Black-Scholes equation؛ Laplace transform؛ Global error؛ Numerical integration؛ State feedback؛ Adaptive step size؛ Eigenvalues as signment؛ Certainty matrix
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