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A complement to the Grigoriev theorem for the Kabanov model

Lépinette, Emmanuel; Zhao, Jun (2020), A complement to the Grigoriev theorem for the Kabanov model, Theory of Probability and Its Applications, 65, 2, p. 322–329. 10.1137/S0040585X97T989969

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Theory of Probability and Its Applications
Volume
65
Number
2
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
322–329
Publication identifier
Metadata
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Author(s)
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zhao, Jun
Department of Polymer Science and Engineering [USTB]
Abstract (EN)
We provide an equivalent characterisation of absence of arbitrage opportunity NA for the Bid and Ask financial market model analog to the Dalang--Morton--Willinger theorem formulated for discrete-time financial market models without friction. This result completes the Grigoriev theorem for conic models in the two dimensional case by showing that the set of all terminal liquidation values is closed under NA.
Subjects / Keywords
Financial market models; Liquidation value; Transaction costs; Absence of arbitrage opportunities; and phrases: Proportional transaction costs; Bid and ask prices; Consis-tent price systems