Essential supremum and essential maximum with respect to random preference relations |
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Authors: | Yuri Kabanov Emmanuel Lépinette |
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Institution: | 1. University of Franche Comté, Laboratoire de Mathématiques, 16 Route de Gray, 25030 Besançon cedex, France;2. National Research University Higher School of Economics, International Laboratory of Quantitative Finance, Moscow, Russia;3. Paris-Dauphine University, Ceremade, Place du Maréchal De Lattre De Tassigny, 75775 Paris cedex 16, France |
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Abstract: | In the first part of the paper, we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility representations. In the second part of the paper, we consider partial orders and preference relations “lifted” from a metric separable space X endowed by a random preference relation to the space L0(X) of X-valued random variables. We provide an example of application of the notion of essential maximum to the problem of the minimal portfolio super-replicating an American-type contingent claim under transaction costs. |
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Keywords: | Preference relation Partial order Random cones Transaction costs American option Hedging |
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