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Random optimization on random sets

Lépinette, Emmanuel (2020), Random optimization on random sets, Mathematical Methods of Operations Research, 91, p. 159-173. 10.1007/s00186-019-00686-6

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Mathematical Methods of Operations Research
Volume
91
Publisher
Springer
Pages
159-173
Publication identifier
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Author(s)
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Random sets and random preorders naturally appear in financial market modelling with transaction costs. In this paper , we introduce and study a concept of essential minimum of a family of vector-valued random variables, i.e. the set of all minimal elements with respect to some random preorder. We provide some conditions under which the essential minimum is not empty and we present two applications in optimisation to Mathematical Finance and Economics.
Subjects / Keywords
Random preference relations; Random sets; Super hedging; Transaction costs; NA2 condition