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Regularity of affine processes on general state spaces


 
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1. Title Title of document Regularity of affine processes on general state spaces
 
2. Creator Author's name, affiliation, country Martin Keller-Ressel; TU Berlin; Germany
 
2. Creator Author's name, affiliation, country Walter Schachermayer; University of Vienna; Austria
 
2. Creator Author's name, affiliation, country Josef Teichmann; ETH Zurich; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) affine process, regularity, semimartingale, generalized Riccati equation
 
3. Subject Subject classification 60J25
 
4. Description 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 $R^d$. 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 $D = R_+^m \times R^n$ 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 $R_+^m \times R^n$ and provide a new probabilistic approach to regularity.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ETH Foundation, Austrian Science Fund (FWF), European Research Council (ERC), Vienna Science and Technology Fund (WWTF), Christian Doppler Research Association (CDG)
 
7. Date (YYYY-MM-DD) 2013-03-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2043
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2043
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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