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.
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Notes
i.e., \(\L (x+y)\ge \L (x)+\L (y)\).
Absence of arbitrage of second kind.
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Lepinette, E. Random optimization on random sets. Math Meth Oper Res 91, 159–173 (2020). https://doi.org/10.1007/s00186-019-00686-6
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DOI: https://doi.org/10.1007/s00186-019-00686-6