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Milstein scheme for the numerical solution of first-order uncertain stochastic differential equations in stock price simulation | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 مهر 1404 | ||
| نوع مقاله: Special Issue-DEDS 17th | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2025.29406.1763 | ||
| نویسنده | ||
| Azadeh Ghasemifard* | ||
| department of applied mathematics, university of Mazandaran, Babolsar, Iran | ||
| تاریخ دریافت: 13 خرداد 1404، تاریخ بازنگری: 03 مهر 1404، تاریخ پذیرش: 05 مهر 1404 | ||
| چکیده | ||
| Uncertain stochastic calculus is a developing branch of mathematics that aims to create models incorporating both aleatory (random) and epistemic (knowledge-based) uncertainties within dynamic systems. In essence, it recognizes two types of uncertainty related to dynamical systems: randomness and belief degree. The uncertain stochastic differential equation (USDE) models such systems by simultaneously integrating randomness and human uncertainty, expressed as belief degree. This growing field has introduced a novel class of equations called USDEs. Since finding exact or analytical solutions to these equations is often difficult, numerical methods provide a practical alternative for approximating solutions. This paper investigates the use of the Milstein method for solving USDEs. Specifically, the Milstein scheme is employed to address a stock pricing problem, and its results are compared with those obtained through the fourth-order Runge-Kutta and Euler methods. The results indicate that the Milstein method yields subtle estimates of stock prices. | ||
| کلیدواژه‌ها | ||
| Chance measure؛ uncertain stochastic differential equation؛ Milstein scheme؛ uncertain stock market | ||
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