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Inhomogeneous affine Volterra processes

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  • Ackermann, Julia
  • Kruse, Thomas
  • Overbeck, Ludger

Abstract

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,Xs) and σ(s,Xs). In the case of affine b and σσT 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)=K¯(t−s) we establish existence of a solution to the stochastic inhomogeneous Volterra equation. If in addition b and σσT 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.

Suggested Citation

  • Ackermann, Julia & Kruse, Thomas & Overbeck, Ludger, 2022. "Inhomogeneous affine Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 250-279.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:250-279
    DOI: 10.1016/j.spa.2022.04.011
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    References listed on IDEAS

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