Random optimization on random sets

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 so...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Germany), 2020-02, Vol.91 (1), p.159-173
Main Author: Lepinette, Emmanuel
Format: Article
Language:English
Subjects:
Business and Management
Calculus of Variations and Optimal Control
Optimization
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Optimization
Original Article
Random variables
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Summary: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.
ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-019-00686-6