对均值回归CEV过程进行显式近似
Approximating explicitly the mean reverting CEV process
AI总结：
本文基于半离散方法改进均值回归CEV过程的显式数值解，构造保持正性的方案并证明其收敛性，通过实验验证并与其他方法比较，最终应用于二维随机波动率模型。
摘要：
本文旨在进一步发展Halidias和Stamatiou（2015）提出的半离散方法。我们关注均值回归CEV过程的数值解，这些过程出现在金融数学模型中，描述为非负解的随机微分方程，具有亚线性扩散系数的形式(x_t)^q，其中1/2<q<1。我们的目标是构造保持正性的显式数值方案。我们证明所提出的SD方案收敛性，其收敛速率取决于参数q。此外，我们通过数值实验验证我们的发现，并与其他保持正性方案进行比较。最后，我们展示如何处理整个二维随机波动率模型，其中即时方差过程由上述均值回归CEV过程给出。
英文摘要：
In this paper we want to exploit further the semi-discrete method appeared in Halidias and Stamatiou (2015). We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics models and are described as non negative solutions of certain stochastic differential equations with sub-linear diffusion coefficients of the form $(x_t)^q,$ where $\frac{1}{2}<q<1.$ Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameter $q.$ Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the whole two-dimensional stochastic volatility model, with instantaneous variance process given by the above mean reverting CEV process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
