Martin Keller-Ressel (ETH Zürich): Affine Processes are Regular

 Affine Processes are a class of Markov processes with important applications in finance and other fields. These processes have been described and fully characterized by Duffie, Filipovic and Schachermayer (2003) under the condition of 'regularity'. Here, a Markov process is called regular, if its characteristic function is differentiable in time with (space-)continuous derivatives. In joint work with Walter Schachermayer and Josef Teichmann I have shown that for affine processes this condition is automatically fulfilled, i.e. that every affine process is regular. The regularity problem has interesting connections to Hilbert's fifth problem on the differentiability of continuous transformation groups, from which we borrow some tools that are unusual in the field of stochastics. Recently the technique of our proof has been successfully applied to show regularity of matrix-valued affine processes