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Application of Stochastic Runge-Kutta Methods for Mixed Fractional Brownian Motion Processes | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 آبان 1404 اصل مقاله (1.28 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.68151.3287 | ||
| نویسندگان | ||
| Nader Karimi* 1؛ Masoumeh Shahmoradi2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, Iran. | ||
| 2Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. | ||
| چکیده | ||
| We develop and analyze a stochastic Runge-Kutta (SRK) method for pricing derivatives when the underlying asset follows a mixed fractional Brownian motion (fBm). From this non‑Markovian process, we re‑derive a Black-Scholes‑type partial differential equation (PDE) and show that the proposed SRK integrator is both mean‑square stable and strongly convergent. Sharp bounds for the stability region and the order of convergence are rigorously proved. Numerical experiments confirm the theory and demonstrate the superior accuracy of the SRK method compared with Euler-Maruyama and Milstein schemes. | ||
| کلیدواژهها | ||
| Stochastic Runge-Kutta (SRK),Black-Scholes model؛ Euler-Maruyama and Milstein schemes, mixed Fractional Brownian motion(mFBm) | ||
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آمار تعداد مشاهده مقاله: 81 تعداد دریافت فایل اصل مقاله: 67 |
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