No arbitrage and multiplicative special semimartingales

Platen, E; Tappe, S

No arbitrage and multiplicative special semimartingales

Platen, E

Tappe, S

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Publisher:: Cambridge University Press (CUP)
Publication Type:: Journal Article
Citation:: Advances in Applied Probability, 2023, 55, (3), pp. 1-42
Issue Date:: 2023-01-01

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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	2023-08-23T02:26:14Z
dc.date.available	2023-08-23T02:26:14Z
dc.date.issued	2023-01-01
dc.identifier.citation	Advances in Applied Probability, 2023, 55, (3), pp. 1-42
dc.identifier.issn	0001-8678
dc.identifier.issn	1475-6064
dc.identifier.uri	http://hdl.handle.net/10453/171814
dc.description.abstract	Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite-variation part of the multiplicative decomposition of the deflator.
dc.language	en
dc.publisher	Cambridge University Press (CUP)
dc.relation.ispartof	Advances in Applied Probability
dc.relation.isbasedon	10.1017/apr.2022.62
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics, 0104 Statistics
dc.subject.classification	Statistics & Probability
dc.subject.classification	4901 Applied mathematics
dc.subject.classification	4905 Statistics
dc.title	No arbitrage and multiplicative special semimartingales
dc.type	Journal Article
utslib.citation.volume	55
utslib.for	0102 Applied Mathematics
utslib.for	0104 Statistics
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	*
dc.date.updated	2023-08-23T02:26:13Z
pubs.issue	3
pubs.publication-status	Published
pubs.volume	55
utslib.citation.issue	3

Abstract:

Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite-variation part of the multiplicative decomposition of the deflator.

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http://hdl.handle.net/10453/171814