Probability Theory and Related Fields

, Volume 151, Issue 3–4, pp 591–611 | Cite as

Affine processes are regular

  • Martin Keller-Ressel
  • Walter Schachermayer
  • Josef Teichmann
Article

Abstract

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.

Keywords

Affine processes Regularity Characteristic function Semiflow 

Mathematics Subject Classification (2000)

60J25 39B32 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Martin Keller-Ressel
    • 1
  • Walter Schachermayer
    • 2
  • Josef Teichmann
    • 1
  1. 1.ETH Zürich, D-MathZürichSwitzerland
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria

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