Path properties and regularity of affine processes on general state spaces

TL;DR

This paper establishes new regularity results for affine processes on general state spaces using Markovian semimartingale methods, and confirms the existence of càdlàg versions under the standard affine process definition.

Contribution

It provides a new proof of regularity for affine processes and shows that the standard definition implies càdlàg paths, resolving longstanding open issues.

Findings

Affine processes are regular under broad conditions.

Existence of càdlàg versions follows from the standard definition.

New proof techniques connect affine processes with Markovian semimartingales.

Abstract

We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-Laplace transform, already implies the existence of a c\`adl\`ag version. This was one of the last open issues in the fundaments of affine processes.