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