SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 79-109, January 2021.
In this paper, to cope with the shortage of sufficient theoretical support resulting from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their well-posedness of strong solutions, and conduct the stability analysis with respect to small perturbations. In the first class, a multidimensional path-dependent process is driven by another multidimensional path-dependent process. The second class is a generalized one-dimensional stochastic volatility model with Hölder continuous coefficients. What greatly differentiates these two classes of models is that both the process and its correlated driving process have their own subdifferential operators, whose one special case is the general reflection operators for multisided barriers. Hence, the models investigated fully cover various newly explored variants of stochastic volatility models whose well-posedness is unknown, and naturally serve as the rigorous mathematical foundation for new stochastic volatility model development in terms of multidimensions, path dependence, and multisided barrier reflection.

中文翻译：

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两类广义随机波动率模型的适定性和稳定性分析

SIAM 金融数学杂志，第 12 卷，第 1 期，第 79-109 页，2021 年 1 月。
在本文中，针对快速增长的量化金融模型导致的理论支持不足，我们研究了两类广义随机波动率模型，建立了它们的强解适定性，并对其进行稳定性分析。小扰动。在第一类中，多维路径依赖过程由另一个多维路径依赖过程驱动。第二类是具有 Hölder 连续系数的广义一维随机波动率模型。这两类模型的最大区别在于过程及其相关驱动过程都有自己的次微分算子，其一个特例是多边障碍的一般反射算子。因此，