A note on the Esscher transform of affine Markov processes

TL;DR

This paper refines the understanding of affine Markov processes by characterizing their martingale property and non-explosion conditions through minimal solutions of Riccati equations, improving previous theoretical results.

Contribution

It provides the final enhancement of earlier results by precisely linking process properties to solutions of Riccati differential equations for affine models.

Findings

Martingale property characterized by minimal Riccati solutions

Non-explosion conditions linked to Riccati equation minimality

Improved theoretical framework for affine processes on canonical spaces

Abstract

In affine models, both the martingale property of stochastic exponentials and non-explosion of affine processes is characterized in terms of minimality of solutions to a system of generalized Riccati differential equations. This is the final improvement of previous results by Duffie, Filipovic and Schachermayer (2003), Mayerhofer, Muhle-Karbe and Smirnov (2011) and Keller-Ressel and Mayerhofer (2015) for processes on canonical state spaces.