Affine realizations with affine state processes for stochastic partial differential equations

Abstract

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results.

27 pages

References in corpus (3)

• An alternative approach on the existence of affine realizations for HJM term structure models
• Real-world forward rate dynamics with affine realizations
• Existence of affine realizations for Lévy term structure models

Cited by in corpus (3)

• Infinite dimensional affine processes
• Invariance of closed convex cones for stochastic partial differential equations
• Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces