Regularity of affine processes on general state spaces

摘要

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 $D = R_+^m imes?R^n$ 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 $R_+^m imes R^n$ and provide a new probabilistic?approach to regularity.