Super-hedging a European option with a coherent risk-measure and without no-arbitrage condition

Emmanuel Lépinette (1) , Jun Zhao

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we revisit the discrete-time super hedging problem of contingent claims with respect to a dynamic risk-measure defined by its acceptance sets. Without any no-arbitrage condition, we show that it is possible to characterize the prices of an European claim. Our analysis reveals a natural weak no-arbitrage condition that we study. This is a condition formulated for the prices instead of the attainable claims. Our approach is not based on a robust representation of the risk-measure and we do not suppose the existence of a risk-neutral probability measure.

Mots clés: Risk-hedging prices; Dynamic risk-measures; Absence of immediate profit; Random sets; Conditional essential supremum

Domaines: Probabilités [math.PR]

Emmanuel Lépinette, Jun Zhao. Super-hedging a European option with a coherent risk-measure and without no-arbitrage condition. 2019. ⟨hal-02379707v1⟩