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dc.date.accessioned2020-05-03T19:16:38Z
dc.date.available2020-05-03T19:16:38Z
dc.date.created2019-12-16T10:29:19Z
dc.date.issued2019
dc.identifier.citationDraouil, Olfa Øksendal, Bernt . A white noise approach to optimal insider control of systems with delay. Journal of Mathematical Analysis. 2019, 476, 101-119
dc.identifier.urihttp://hdl.handle.net/10852/75062
dc.description.abstractWe use a white noise approach to study the problem of optimal insider control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particular, we use Hida-Malliavin calculus and the Donsker delta functional to study the problem. We establish a sufficient and a necessary maximum principle for the optimal control when the trader from the beginning has inside information about the future value of some random variable related to the system. These results are applied to the problem of optimal inside harvesting control in a population modelled by a stochastic delay equation. Next, we apply a direct white noise method to find the logarithmic utility optimal insider portfolio in a generalized Black-Scholes type financial market. A classical result of Pikovski and Karatzas shows that when the inside information is , where T is the terminal time of the trading period, then the market is not viable, i.e. the maximal utility is infinite. We consider two extensions to delay of this result and prove the following: If the risky asset price is given by a stochastic delay equation, the resulting insider market is still not viable. If, however, there is delay in the information flow to the insider, the market becomes viable.
dc.languageEN
dc.publisherUniversiteti i Prishtines
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleA white noise approach to optimal insider control of systems with delay
dc.typeJournal article
dc.creator.authorDraouil, Olfa
dc.creator.authorØksendal, Bernt
cristin.unitcode185,15,13,0
cristin.unitnameMatematisk institutt
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode1
dc.identifier.cristin1761036
dc.identifier.bibliographiccitationinfo:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal of Mathematical Analysis&rft.volume=476&rft.spage=101&rft.date=2019
dc.identifier.jtitleJournal of Mathematical Analysis
dc.identifier.volume476
dc.identifier.issue1
dc.identifier.startpage101
dc.identifier.endpage119
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2019.02.065
dc.identifier.urnURN:NBN:no-78142
dc.type.documentTidsskriftartikkel
dc.type.peerreviewedPeer reviewed
dc.source.issn2217-3412
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/75062/4/1-s2.0-S0022247X19301970-main.pdf
dc.type.versionPublishedVersion
dc.relation.projectNFR/250768


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