论文标题
两类广义随机波动率模型的适应性和稳定性分析
Well-posedness and Stability Analysis of Two Classes of Generalized Stochastic Volatility Models
论文作者
论文摘要
在本文中，为了应对快速增长的定量财务建模产生的足够理论支持的短缺，我们研究了两类的广义随机波动率模型，建立了其强大解决方案的良好性，并就小扰动进行了稳定分析。在第一类中，多维路径依赖性过程是由另一个多维路径依赖性过程驱动的。第二类是具有Hölder连续系数的广义一维随机波动率模型。这两个类别的模型极大地区别在于，该过程及其相关的驾驶过程都有其自己的子差异操作员，其一种特殊情况是多面屏障的一般反射操作员。因此，所研究的模型完全涵盖了各种新探索的随机波动性模型的变体，这些模型尚不清楚，并且在多维，路径依赖性和多领域的屏障反映方面，自然而然地作为新的随机波动性模型开发的严格数学基础。
In this paper, to cope with the shortage of sufficient theoretical support resulted 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 those 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 multi-sided 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 multi-dimension, path-dependence, and multi-sided barrier reflection.
