<div class="csl-bib-body">
<div class="csl-entry">Wiedermann, K. (2021). <i>Deep learning techniques in portfolio optimization under constraints</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2021.79823</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2021.79823
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/18318
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dc.description.abstract
We consider the constrained utility maximization problem and the corresponding dual problem with regard to theoretical results which allow the formulation of algorithmic solvers which make use of deep learning techniques. We place great emphasis on detailed proofs of the underlying theoretical results. At first, the deep controlled 2BSDE algorithm from [5] is derived in a Markovian setting. It combines the dynamic programming approach with the adjoint equation from the stochastic maximum principle (SMP). In the case of random coefficients, we prove stochastic maximum principles for the primal and the dual problem, respectively. Furthermore, we show that the strong duality property holds under additional assumptions. This leads to the formulation of the deep SMP algorithm as in [5]. Moreover, we use the aforementioned result for the primal problem for defining a new algorithm, which we call deep primal SMP algorithm. Numerical examples illustrate the effectiveness of the studied algorithms - in particular for higher-dimensional problems and problems with random coefficients, which are either path dependent or satisfy their own SDEs. Moreover, our numerical experiments for constrained problems show that the novel deep primal SMP algorithm overcomes the deep SMP algorithm's weakness of erroneously producing the value of the corresponding unconstrained problem. Furthermore, in contrast to the deep controlled 2BSDE algorithm, this algorithm is also applicable to problems with path dependent coefficients. As the deep primal SMP algorithm even yields the most accurate results in many of our studied problems, we can highly recommend its usage.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Portfoliooptimierung unter Restriktionen
de
dc.subject
Nutzenmaximierungsproblem
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dc.subject
duales Problem
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dc.subject
Deep Learning
de
dc.subject
maschinelles Lernen
de
dc.subject
stochastisches Maximumprinzip
de
dc.subject
Ansatz der stochastischen Steuerung
de
dc.subject
Portfolio optimization under constraints
en
dc.subject
utility maximization problem
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dc.subject
dual problem
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dc.subject
deep learning
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dc.subject
machine learning
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dc.subject
stochastic maximum principle
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dc.subject
dynamic programming approach
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dc.title
Deep learning techniques in portfolio optimization under constraints
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2021.79823
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Kristof Wiedermann
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC16310701
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dc.description.numberOfPages
118
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.mimetype
application/pdf
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item.cerifentitytype
Publications
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item.openairetype
master thesis
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item.languageiso639-1
en
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item.fulltext
with Fulltext
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item.openaccessfulltext
Open Access
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item.grantfulltext
open
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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crisitem.author.dept
E105-01 - Forschungsbereich Risikomanagement in Finanz- und Versicherungsmathematik
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik