2011/05/03 by Martin Keller-Ressel, Martin Keller‐Ressel, Walter Schachermayer +4
Economics, Econometrics and Finance · Mathematics · #60J25 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J25
paper · pdf · doi:10.48550/arxiv.1105.0632
minor corrections
openalex publication_date 2011/05/03 · arxiv created 2012/05/22 · arxiv updated 2012/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 = R+m × 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 R+m × Rn and provide a new probabilistic approach to regularity.