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
TypeArticle accepté pour publication ou publié
Journal nameTheory of Probability and Its Applications
SIAM - Society for Industrial and Applied Mathematics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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 / KeywordsFinancial market models; Liquidation value; Transaction costs; Absence of arbitrage opportunities; and phrases: Proportional transaction costs; Bid and ask prices; Consis-tent price systems
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