Consistent Risk Measure on L 0 : NA Condition, Pricing and Dual Representation

Emmanuel Lépinette (1) , Duc Thinh Vu

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on L0 is fixed to characterize the family of acceptable wealths that play the role of non negative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices of an European option. Moreover we provide an example where it is possible to obtain a dual representation of the risk-measure on L0 .

Mots clés: NA condition; Risk-hedging prices; Dynamic risk-measures; Dual representation; No-arbitrage; NA condition

Domaines: Probabilités [math.PR]

Emmanuel Lépinette, Duc Thinh Vu. Consistent Risk Measure on L 0 : NA Condition, Pricing and Dual Representation. International Journal of Theoretical and Applied Finance, 2021, 24 (06n07), ⟨10.1142/S0219024921500370⟩. ⟨hal-02976860⟩