On symbols and uniqueness of polynomial processes - an example
Event details
| Date | 17.06.2014 |
| Hour | 12:00 › 13:00 |
| Speaker | Paul KRÜHNER (University of Oslo) |
| Location | |
| Category | Conferences - Seminars |
Polynomial processes are in principle a generalisation of affine processes. Both these process types are used in financial modelling. The class of polynomial processes includes - unlike affine processes - the geometric Brownian motion and the Dunkl process. The Markovian characteristics of polynomial processes has to satisfy certain polynomial conditions and all power moments of polynomial processes do exists and can be computed in closed form from its Markovian characteristics. In this talk we present an example of two polynomial processes on the real line which are different in law but do have the same Markovian characteristics. In particular, even though the Markovian characteristics of a polynomial process does determine all power moments it does not determine its law. Subsequently, we will discuss the symbol - the time derivative of the characteristic function at time zero - and second order polynomial processes. This class includes all polynomial processes with continuous sample paths. Finally, we do investigate a new semi-Fourier based approach which allows to show that some second order processes are determined by their Markovian characteristics. This talk is based on joint work with Prof. Jan Kallsen.
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