A complement to the Grigoriev theorem for the Kabanov model.

Emmanuel Lépinette (1) , Jun Zhao (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 USTB - Department of Polymer Science and Engineering

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..

Mots clés: Liquidation value; Transaction costs; Absence of arbitrage opportunities; Financial market models; and phrases: Proportional transaction costs; Bid and ask prices; Consis-tent price systems

Domaines: Probabilités [math.PR]

Emmanuel Lépinette, Jun Zhao. A complement to the Grigoriev theorem for the Kabanov model.. SIAM Theory of Probability and its Applications, 2020. ⟨hal-01666860v6⟩