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

Lépinette, Emmanuel; Zhao, Jun (2022), Super-hedging a European option with a coherent risk-measure and without no-arbitrage condition, Stochastics: An International Journal of Probability and Stochastic Processes, p. 36. 10.1080/17442508.2022.2055966

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Stochastics: An International Journal of Probability and Stochastic Processes
Publisher
Taylor & Francis
Published in
Paris
Pages
36
Publication identifier
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Author(s)
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zhao, Jun
Department of Polymer Science and Engineering [USTB]
Abstract (EN)
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.
Subjects / Keywords
Risk-hedging prices; Dynamic risk-measures; Absence of immediate profit; Random sets; Conditional essential supremum; and phrases: Risk-hedging prices; Conditional essential infi- mum Mathematics Subject Classification (2010): 49J53; 60D05; 91G20; 91G80 JEL Classification: C02; C61; G13