Affine processes are regular
By Martin Keller‐Ressel, Walter Schachermayer, Josef Teichmann. 2009
78 citations recorded by the source corpus.
We show that stochastically continuous, time-homogeneous affine processes on the canonical state space $${\mathbb{R}_{\geq 0}^m \times \mathbb{R}^n}$$ are always regular. In the paper of Duffie et al. (Ann Appl Probab 13(3):984–1053, 2003) regularity was used as a crucial basic assumption. It was left open whether this regularity condition is automatically satisfied for stochastically continuous affine processes. We now show that the regularity assumption is indeed superfluous, since regularity follows from stochastic continuity and the exponentially affine form of the characteristic function. For the proof we combine classic results on the differentiability of transformation semigroups with the method of the moving frame which has been recently found to be useful in the theory of SPDEs.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/9d6aee7358c4c98a809347a51b11f6cac381d6cb
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Citations in the corpus
- Affine Processes on Positive Semidefinite Matrices (2009, unknown): “The Feller property is then a simple consequence of this statement and regularity is obtained by arguing as in Keller-Ressel, Schachermayer and Teichmann [35], who obtained the corresponding statements for affine processes on the state space R+ × R; see [35], Theorem 4.”
- Continuous-State Branching Processes with Immigration (2019, background): “The regularity problem was settled in Keller-Ressel et al. (2011), where it was proved that any stochastically continuous affine process is regular.”