论文标题
不均匀的仿射伏特拉工艺
Inhomogeneous affine Volterra processes
论文作者
论文摘要
我们将有关仿射伏特拉过程的最新结果扩展到不均匀的情况。这包括由布朗运动驱动的摩擦式方程解决方案的力矩界限，并具有不均匀的内核$ k（t，s）$和不均匀的漂移和扩散系数$ b（s，x_s）$和$σ（s，s，x_s）$。对于Aggine $ b $和$σσ^t $，我们展示了如何通过不均匀的Riccati-volterra积分方程的解决方案来表示条件傅立叶宽度功能。对于卷积类型$ k（t，s）= \ overline {k}（t-s）$的内核，我们为随机不均匀的Volterra方程建立了解决方案。如果另外，$ b $和$σσ^t $是仿射，我们证明有条件的傅立叶 - 拉普拉斯功能在过去的路径中是指数级的。最后，我们将这些结果应用于数学金融中使用的粗糙赫斯顿模型的不均匀扩展。
We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an inhomogeneous kernel $K(t,s)$ and inhomogeneous drift and diffusion coefficients $b(s,X_s)$ and $σ(s,X_s)$. In the case of affine $b$ and $σσ^T$ we show how the conditional Fourier-Laplace functional can be represented by a solution of an inhomogeneous Riccati-Volterra integral equation. For a kernel of convolution type $K(t,s)=\overline{K}(t-s)$ we establish existence of a solution to the stochastic inhomogeneous Volterra equation. If in addition $b$ and $σσ^T$ are affine, we prove that the conditional Fourier-Laplace functional is exponential-affine in the past path. Finally, we apply these results to an inhomogeneous extension of the rough Heston model used in mathematical finance.
