Department of Pattern Recognition

(eng): In this paper, we introduce notion of progressive projection, closely related to the extended predictable projection. This notion is exible enough to help us treat the problem of log-optimal investment without transaction costs almost exhaustively in case when the rate of return is not observed. We prove some results saying that the semimartingale property of a continuous process is preserved when changing the filtration to the one generated by the process under very general conditions. We also had to introduce a very useful and exible notion of so called enriched filtration.