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Theory of Stochastic Processes, 2020, Volume 25(41), Issue 1, Pages 37–77 (Mi thsp311)  
Progressive projection and log-optimal investment in the frictionless market

P. Dostálab, T. Macha

a Institute of Information Theory and Automation, Czech Academy of Science, Prague, Czech Republic
b Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic
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Abstract: 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.
Keywords: Log-optimal investment, progressive projection, filtering.
Document Type: Article
MSC: 60H30, 60G44, 91G80
Language: English
Citation: P. Dostál, T. Mach, “Progressive projection and log-optimal investment in the frictionless market”, Theory Stoch. Process., 25(41):1 (2020), 37–77
Citation in format AMSBIB
\Bibitem{DosMac20}
\by P.~Dost\'al, T.~Mach
\paper Progressive projection and log-optimal investment in the frictionless market
\jour Theory Stoch. Process.
\yr 2020
\vol 25(41)
\issue 1
\pages 37--77
\mathnet{http://mi.mathnet.ru/thsp311}
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