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August 2021 Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels
Eduardo Abi Jaber
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Bernoulli 27(3): 1583-1615 (August 2021). DOI: 10.3150/20-BEJ1284

Abstract

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L1-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is based on approximations using stochastic Volterra equations with L2-kernels combined with a general stability result. Most importantly, we establish weak uniqueness using a duality argument on the Fourier–Laplace transform via a deterministic Riccati–Volterra integral equation. We illustrate the applicability of our results on Hawkes processes and a class of hyper-rough Volterra Heston models with a Hurst index H(1/2,1/2].

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Eduardo Abi Jaber. "Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels." Bernoulli 27 (3) 1583 - 1615, August 2021. https://doi.org/10.3150/20-BEJ1284

Information

Received: 1 December 2019; Revised: 1 June 2020; Published: August 2021
First available in Project Euclid: 10 May 2021

Digital Object Identifier: 10.3150/20-BEJ1284

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 3 • August 2021
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