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2013 Regularity of affine processes on general state spaces
Martin Keller-Ressel, Walter Schachermayer, Josef Teichmann
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Electron. J. Probab. 18: 1-17 (2013). DOI: 10.1214/EJP.v18-2043

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.

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Martin Keller-Ressel. Walter Schachermayer. Josef Teichmann. "Regularity of affine processes on general state spaces." Electron. J. Probab. 18 1 - 17, 2013. https://doi.org/10.1214/EJP.v18-2043

Information

Accepted: 26 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1291.60153
MathSciNet: MR3040553
Digital Object Identifier: 10.1214/EJP.v18-2043

Subjects:
Primary: 60J25

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