英文标题：
《Markovian lifts of positive semidefinite affine Volterra type processes》
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作者：
Christa Cuchiero and Josef Teichmann
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最新提交年份：
2019
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英文摘要：
  We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \\cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein Uhlenbeck processes whose state space are matrix valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston type model.
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中文摘要：
我们从广义Feller性质的角度考虑出现为矩阵值（仿射）Volterra型过程的马尔可夫提升的随机偏微分方程（参见例{doetei:10}）。我们特别介绍了半正定矩阵锥中具有分数核和值的Volterra-Wishart过程。它们由状态空间为矩阵值测度的无限维Ornstein-Uhlenbeck过程的矩阵积构造而成。与此平行，我们还考虑了正定Volterra纯跳跃过程，从而产生了多元Hawkes型过程。我们将这些仿射协方差过程应用于多元（粗糙）波动率建模，并引入了一个（粗糙）多元Volterra-Heston模型。
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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