
Open access
Date
2013Type
- Journal Article
Abstract
We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state space D, i.e. an arbitrary Borel subset of Rd. We show that such a process is always regular, meaning that its Fourier-Laplace transform is differentiable in time, with derivatives that are continuous in the transform variable. As a consequence, we show that generalized Riccati equations and Levy-Khintchine parameters for the process can be derived, as in the case of D=Rm+×Rn studied in Duffie, Filipovic and Schachermayer (2003). Moreover, we show that when the killing rate is zero, the affine process is a semi -martingale with absolutely continuous characteristics up to its time of explosion. Our results generalize the results of Keller-Ressel, Schachermayer and Teichmann (2011) for the state space Rm+×Rn and provide a new probabilistic approach to regularity. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000043966Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
Affine process; Regularity; Semimartingale; Generalized Riccati equationOrganisational unit
03845 - Teichmann, Josef / Teichmann, Josef
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