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

TL;DR

This paper studies Markovian lifts of affine Volterra processes with jumps, establishing new existence, uniqueness, and approximation results, and showing that the theory becomes more classical in this Markovian framework.

Contribution

It introduces new theoretical results for Markovian lifts of affine Volterra processes with jumps, expanding the understanding of their properties and approximations.

Findings

Proved new existence and uniqueness results for Markovian lifts.

Developed approximation methods for affine rough volatility models.

Showed the classical nature of stochastic Volterra processes in the Markovian setting.

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.~\cite{doetei:10}. 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.