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تسجيل مستخدم جديدInhomogeneous affine Volterra processes
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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 $sigma(s,X_s)$. In the case of affine $b$ and $sigma sigma^T$ 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 $sigma sigma^T$ 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.
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