No-arbitrage concepts in topological vector lattices

Platen, E; Tappe, S

No-arbitrage concepts in topological vector lattices

Platen, E

Tappe, S

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Publisher:: Springer Science and Business Media LLC
Publication Type:: Journal Article
Citation:: Positivity, 2021, 25, (5), pp. 1853-1898
Issue Date:: 2021-07-03

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Field	Value	Language
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123
dc.contributor.author	Tappe, S
dc.date.accessioned	2021-12-02T02:51:31Z
dc.date.available	2021-12-02T02:51:31Z
dc.date.issued	2021-07-03
dc.identifier.citation	Positivity, 2021, 25, (5), pp. 1853-1898
dc.identifier.issn	1385-1292
dc.identifier.issn	1572-9281
dc.identifier.uri	http://hdl.handle.net/10453/152024
dc.description.abstract	We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA1 and NA1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.
dc.language	en
dc.publisher	Springer Science and Business Media LLC
dc.relation.ispartof	Positivity
dc.relation.isbasedon	10.1007/s11117-021-00848-z
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics, 0102 Applied Mathematics
dc.subject.classification	General Mathematics
dc.title	No-arbitrage concepts in topological vector lattices
dc.type	Journal Article
utslib.citation.volume	25
utslib.for	0101 Pure Mathematics
utslib.for	0102 Applied Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access	*
pubs.consider-herdc	true
dc.date.updated	2021-12-02T02:51:30Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	25
utslib.citation.issue	5

Abstract:

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA1 and NA1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/152024