Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels

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