Abstract.
In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively.
On the technical level, an important role is played by \(\sigma\)-sub- and \(\sigma\)-supermartingales. We characterize these processes in terms of semimartingale characteristics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: June 2003,
Mathematics Subject Classification (2000):
91B24, 60G48, 91B16, 91A15, 60G40
JEL Classification:
G13, D52, C73
The authors want to thank PD Dr. Martin Beibel for the idea leading to the proof of Proposition A.4 and both anonymous referees for many valuable comments. The second author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg Angewandte Algorithmische Mathematik at Munich University of Technology and by the Fonds zur Förderung der wissenschaftlichen Forschung at Vienna University of Technology.
Rights and permissions
About this article
Cite this article
Kallsen, J., Kühn, C. Pricing derivatives of American and game type in incomplete markets. Finance and Stochastics 8, 261–284 (2004). https://doi.org/10.1007/s00780-003-0110-7
Issue Date:
DOI: https://doi.org/10.1007/s00780-003-0110-7