Affine processes on symmetric cones

TL;DR

This paper provides a complete classification of affine Markov processes on symmetric cones, extending the theory of Wishart processes to a broader class of conic state spaces.

Contribution

It characterizes all affine processes on irreducible symmetric cones using Lévy-Khintchine triplets, expanding the understanding of such processes beyond previous specific cases.

Findings

Complete classification of affine processes on symmetric cones

Extension of Wishart process theory to general symmetric cones

Characterization via Lévy-Khintchine triplets

Abstract

We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in an irreducible symmetric cone in terms of certain L\'evy-Khintchine triplets. This is the complete classification of affine processes on these conic state spaces, thus extending the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (1991).