The Dalang–Morton–Willinger version of the fundamental theorem of asset pricing for the Bid-Ask financial market model

Zhao Jun , Emmanuel Lépinette (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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; Bid and Ask prices; Transaction costs; Absence of arbitrage opportunities; Financial market models

Domaines: Probabilités [math.PR]

Zhao Jun, Emmanuel Lépinette. The Dalang–Morton–Willinger version of the fundamental theorem of asset pricing for the Bid-Ask financial market model. 2018. ⟨hal-01666860v4⟩