论文标题
希尔伯特空间中仿射随机协方差模型的固定协方差制度
Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces
论文作者
论文摘要
我们研究了仿射过程对积极的自我加入Hilbert-Schmidt操作员的长期行为，该操作员是纯种类型，保守的，并且是有限的。对于亚临界过程，我们证明存在独特的极限分布并构建相应的固定仿射过程。此外，我们在[1，2] $中的订单$ p \ wasserstein距离中获得了基础过渡内核的显式收敛速率，并为极限分布的前两个矩提供明确的公式。我们将结果应用于对固定协方差制度中无限仿射随机协方差模型的研究，在固定协方差方面，固定仿射过程对瞬时协方差过程进行了建模。在这种情况下，我们研究了在固定收益或Heath-Jarrow-Morton-Musiela框架中提出的固定收益或商品市场中向前曲线动力学建模的几何前向前曲线模型中隐含的向前波动微笑的行为。
We study the long-time behavior of affine processes on positive self-adjoiont Hilbert-Schmidt operators which are of pure-jump type, conservative and have finite second moment. For subcritical processes we prove the existence of a unique limit distribution and construct the corresponding stationary affine process. Moreover, we obtain an explicit convergence rate of the underlying transition kernels to the limit distribution in the Wasserstein distance of order $p\in [1, 2]$ and provide explicit formulas for the first two moments of the limit distribution. We apply our results to the study of infinite-dimensional affine stochastic covariance models in the stationary covariance regime, where the stationary affine process models the instantaneous covariance process. In this context we investigate the behavior of the implied forward volatility smile for large forward dates in a geometric affine forward curve model used for the modeling of forward curve dynamics in fixed income or commodity markets formulated in the Heath-Jarrow-Morton-Musiela framework.
