Pub Date : 2020-12-21DOI: 10.37863/tsp-5988900404-25
P. Dostál, T. Mach
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.
{"title":"Progressive projection and log-optimal investment in the frictionless market","authors":"P. Dostál, T. Mach","doi":"10.37863/tsp-5988900404-25","DOIUrl":"https://doi.org/10.37863/tsp-5988900404-25","url":null,"abstract":"\u0000In this paper, we introduce notion of progressive projection, closely related to the extended predictable projection.\u0000This 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.\u0000We prove some results saying that the semimartingale property of a continuous process is preserved\u0000when changing the filtration to the one generated by the process under very general conditions.\u0000We also had to introduce a very useful and flexible notion of so called enriched filtration.\u0000","PeriodicalId":38143,"journal":{"name":"Theory of Stochastic Processes","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74405996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-12DOI: 10.37863/tsp-5146373507-56
A. Dorogovtsev, M. B. Vovchanskii
We derive representations for finite-dimensional densities of the point process associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentials appearing in the analog of the Girsanov theorem for the Arratia flow.
{"title":"Representations of the finite-dimensional point densities in Arratia flows with drift","authors":"A. Dorogovtsev, M. B. Vovchanskii","doi":"10.37863/tsp-5146373507-56","DOIUrl":"https://doi.org/10.37863/tsp-5146373507-56","url":null,"abstract":"\u0000We derive representations for finite-dimensional densities of the point process associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentials appearing in the analog of the Girsanov theorem for the Arratia flow. \u0000","PeriodicalId":38143,"journal":{"name":"Theory of Stochastic Processes","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89865773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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