Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case

Abstract

We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in, e.g., Dörsek and Teichmann (A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). In particular, we provide new existence, uniqueness and approximation results for Markovian lifts of affine rough volatility models of general jump diffusion type. We demonstrate that in this Markovian light the theory of stochastic Volterra processes becomes almost classical.