Abstracts

In this talk we discuss changes of probability measure up to a random time $\sigma$. Working under the standing assumptions that $\sigma$ avoids stopping times and that all martingales are continuous, we extend results from Mortimer and Williams (1991) and provide new classes of examples involving honest times and pseudo-stopping times. Moreover, we study the stability of the pseudo-stopping time property with respect to certain measure changes.
While changes of measure are ubiquitous in mathematical finance due to the fundamental theorem of asset pricing, enlargements of filtrations are used to model credit risk and insider trading. We therefore investigate the following question: If we assume NFLVR with respect to the original filtration, under which conditions is the market then also arbitrage-free with respect to the progessively enlarged filtration until time $\sigma$? For an honest time $\sigma$ this question was recently studied in detail by Fontana, Jeanblanc and Song (2013). In this talk we consider the case of an arbitrary random time $\sigma$ and a continuous stock price process, and we are able to give sufficient criteria for NFLVR on the time horizon $[0,\sigma]$ in terms of the multiplicative decomposition of the Azéma supermartingale associated with $\sigma$.