As a core tool in the field of financial mathematics, stochastic differential equations (SDEs) not only profoundly depict the complexity and variability of financial markets, but also play an irreplaceable role in the high-end financial engineering of option pricing. SDEs effectively simulate random fluctuations, jump risks, and unpredictable factors in the market by introducing random terms such as Brownian motion or more general Lévy processes, providing a powerful framework for accurate modeling of dynamic processes in financial markets. In the field of option pricing, the application of SDEs is particularly crucial. Taking the Black-Scholes pricing model as an example, it is based on the assumption of geometric Brownian motion and obtains an explicit formula for the price of European options by solving a specific SDE. In addition, the stability analysis of SDEs in option pricing is also one of the research hotspots. Stability is not only related to the reliability of model prediction results, but also directly affects the effectiveness of trading strategies. The in-depth application and stability research of SDEs in financial mathematics, especially in option pricing, is of great significance for promoting the development and innovation of financial markets.

Limengna Liao. The Application and Stability Analysis of Stochastic Differential Equations in Financial Mathematics. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 3: 137-141. https://doi.org/10.25236/AJMS.2024.050315.

[1] Lei Ziqi, Zhou Qing. Research on option pricing based on uncertain fractional differential equations under floating interest rates[J]. Journal of Applied Mathematics, 2022, 45 (03): 401-420.

[2] Wang Xinyi, Guo Zhidong. Pricing of Look Back Options Driven by Secondary Diffusion Processes [J]. Journal of Anqing Normal University (Natural Science Edition), 2022, 28 (03): 59-62.

[3] Wang Xinyi, Guo Zhidong. Pricing Model of European Options with Random Interest Rates under Mixed Fractional Brownian Motion Mechanism[J]. Journal of Anqing Normal University (Natural Science Edition), 2022, 28 (01): 92-98.

[4] Gao Shilei, Li Anqi, He Jialu, et al. Numerical simulation and positive comparative analysis of insurance based on CIR model[J]. Science and Technology Innovation Report, 2020,17 (03): 105-108.

[5] Sun Jiaojiao Mellin Transform Method for Pricing European Options under Vasilek Random Interest Rate Model[J]. Economic Mathematics, 2019,36 (03): 21-26.

[6] Zhang Lingxi, Yin Junfeng Numerical Method of KoBol Fractional Order Option Pricing Model[J]. Journal of Tongji University (Natural Science Edition), 2020, 48 (10): 1495-1505.

[7] Hu Yinggang, Jiang Yanqin, Huang Xiaoqian. 7th order weighted compact nonlinear scheme for non-stationary Hamilton Jacobi equation[J]. Journal of Mechanics, 2022, 54 (11): 3203-3214.

[8] Wang Yao, Xue Hong. Pricing of Fragile Options in the Dual Score Vasicek Interest Rate Environment [J]. Computer and Digital Engineering, 2019, 47 (03): 503-507+519.

[9] Wang Jianing, Xue Hong. Pricing of reload options under fractional Brownian motion[J]. Journal of Hangzhou Normal University (Natural Science Edition), 2019, 18 (02): 180-184.

[10] Lan Haifeng, Xiao Feiyan, Zhang Gengen, et al. Error Analysis of Tight Implicit BDF Method for Nonlinear Partial Integral Differential Equations[J]. Journal of Guangxi Normal University (Natural Science Edition), 2020, 38 (04): 82-91.