Essential supremum and essential maximum with respect to random preference relations

Yuri Kabanov and Emmanuel Lépinette
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Journal of Mathematical Economics, 2013, vol. 49, issue 6, 488-495

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.

Keywords: Preference relation; Partial order; Random cones; Transaction costs; American option; Hedging (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:49:y:2013:i:6:p:488-495

DOI: 10.1016/j.jmateco.2013.05.007

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