Mathematical Finance Seminar

Speaker: Jean Jacod

Title: Is a discretely observed semimartingale Itˆo or not ?

Abstract: In high-frequency statistics, and among various hypotheses, the fact that the underlying observed process is an Itˆo semimartingale is always assumed. Here we want to examine whether this basic hypothesis can be tested, on the basis of discrete observations. This talk is concerned with a rather restrictive setting, in the sense that we restrict our attention mainly to semimartingales that are continuous, and (unfortunately) with the structural feature that it is a time-changed Itˆo semimartingale (this in itself is not a restriction) with a time change which may be random, but is independent of the driving Brownian motion.