Before revision: We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L^1-kernels  . Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance.
After revision: We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L^1-kernels and jumps . Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance.