Infinite dimensional affine processes

TL;DR

This paper investigates infinite dimensional affine diffusion processes, deriving Riccati equations, proving their existence via Hilbert space SDEs, and providing examples, thus filling a gap in the literature.

Contribution

It introduces a framework for infinite dimensional affine processes, including existence proofs and a new version of the Yamada-Watanabe theorem for Hilbert space-valued SDEs.

Findings

Derived Riccati differential equations for these processes

Proved existence of infinite dimensional affine processes

Provided examples illustrating the theory

Abstract

The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada-Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results.