Random optimization on random sets

Emmanuel Lepinette ()
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Emmanuel Lepinette: CEREMADE, Paris-Dauphine University, PSL National Research

Mathematical Methods of Operations Research, 2020, vol. 91, issue 1, No 9, 159-173

Abstract: Abstract Random sets and random preorders naturally appear in financial market modeling with transaction costs. In this paper, we introduce and study a concept of essential minimum for a family of vector-valued random variables, as a set of 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 for mathematical finance and economics.

Keywords: Random preference relations; Random sets; Super-hedging; Transaction costs; NA2 condition; 91G20; 60D05; 60G42 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-019-00686-6

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