Infinite dimensional affine processes

Thorsten Schmidt, Stefan Tappe and Weijun Yu

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7131-7169

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.

Keywords: Infinite dimensional affine process; Canonical state space; Riccati equation; Stochastic differential equation on a Hilbert space; Yamada–Watanabe theorem; Retracted subspace with compact embedding (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.spa.2020.07.009

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