Infinite dimensional affine processes
arXiv:1907.10337 · doi:10.1016/j.spa.2020.07.009
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.
arXiv comment37 pages
References in corpus (5)
- Exponential moments of affine processes
- The Yamada-Watanabe Theorem for mild solutions to stochastic partial differential equations
- Stochastic evolution equations for large portfolios of stochastic volatility models
- Affine realizations with affine state processes for stochastic partial differential equations
- Path properties and regularity of affine processes on general state spaces