Stationary covariance regime for affine stochastic covariance models in Hilbert spaces
在希尔伯特空间中引入具有平稳仿射瞬时协方差过程的随机协方差模型，证明了次临界仿射过程极限分布的存在性，给出了Wasserstein距离下的收敛速率和极限分布的前两阶矩公式，并应用于固定收益和大宗商品市场的远期曲线动态分析。
Abstract This paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order $p \in [1,2]$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>]</mml:mo> </mml:math> , and give explicit formulas for the first two moments of the limit distribution. Our results allow us to introduce affine stochastic covariance models in the stationary covariance regime and to investigate the behaviour of the implied forward volatility for large forward dates in commodity forward markets.