Distribution functions, extremal limits and optimal transport
| Autor: | Maria Rita Iacò, Stefan Thonhauser, Robert F. Tichy |
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| Rok vydání: | 2015 |
| Předmět: |
General Mathematics
Mathematical finance 010102 general mathematics Copula (linguistics) Of the form 010103 numerical & computational mathematics Unit square 01 natural sciences Combinatorics Distribution function Mathematics::Probability Optimization and Control (math.OC) FOS: Mathematics Combinatorial optimization 0101 mathematics Mathematics - Optimization and Control Assignment problem Mathematics Probability measure |
| Zdroj: | Indagationes Mathematicae. 26:823-841 |
| ISSN: | 0019-3577 |
| DOI: | 10.1016/j.indag.2015.05.003 |
| Popis: | Encouraged by the study of extremal limits for sums of the form lim N → ∞ 1 N ∑ n = 1 N c ( x n , y n ) with uniformly distributed sequences { x n } , { y n } the following extremal problem is of interest max γ ∫ [ 0 , 1 ] 2 c ( x , y ) γ ( d x , d y ) , for probability measures γ on the unit square with uniform marginals, i.e., measures whose distribution function is a copula. The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing γ ’s one can give alternative proofs of some results from the field of uniform distribution theory and beyond that treat additional questions. Finally, some applications to mathematical finance are addressed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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