A dual representation of gain–loss hedging for European claims in discrete time

Abstract

Superhedging of European claims in incomplete markets is a well-studied problem. The superhedging value of a European claim is known to yield a price too large to be interesting in some cases. In this note, an alternative hedging strategy based on an expected gain–loss criterion is studied for European claims in infinite state space, discrete time financial markets. A dual representation for the gain–loss hedging value is obtained.

Keywords:

• European claims
• pricing
• gain–loss hedging
• superhedging
• martingales

Acknowledgements

Author was supported in part by a visiting researcher grant from the University of L'Aquila, Italy, made possible by Research Grant Reti per la conoscenza e l'orientamento tecnico-scientifico per lo sviluppo della competitività (RE.C.O.TE.S.S.C.) POR 2007-2013-Action 4, funded by Regione Abruzzo and the European Social Fund 2007-2013. The author is grateful to Savaş Dayanık for useful discussions and to an anonymous referee for a careful review.