Pathwise construction of affine processes

TL;DR

This paper presents a method to construct affine processes explicitly as solutions to time change equations, extending previous theoretical results and providing a stronger representation framework.

Contribution

It offers a strong version of Kallsen's theorem, showing how affine processes can be represented as time-changed Lévy processes based on multivariate time change theory.

Findings

Affine processes can be identified as solutions to specific time change equations.

Provides a stronger, more explicit representation of affine processes.

Extends Kallsen's law-based theorem to a constructive framework.

Abstract

Based on the theory of multivariate time changes for Markov processes, we show how to identify affine processes as solutions of certain time change equations. The result is a strong version of a theorem presented by J. Kallsen (2006) which provides a representation in law of an affine process as a time-change transformation of a family of independent L\'evy processes.