Progressive projection and log-optimal investment in the frictionless market

P. Dostál, T. Mach
Theory of Stochastic Processes
Vol.25 (41), no.1, 2020, pp.37-77
In this paper, we introduce notion of progressive projection, closely related to the extended predictable projection. This notion is flexible 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 flexible notion of so called enriched filtration.
DOI: https://doi.org/10.37863/tsp-5988900404-25
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