On the pointwise supremum of the set of copulas with a given curvilinear section
Yao Ouyang, Yonghui Sun, Hua-Peng Zhang
TL;DR
This paper derives an explicit formula for the pointwise supremum of copulas with a specified curvilinear section, characterizing when this supremum is itself a copula and its relation to the greatest quasi-copula.
Contribution
It provides a novel explicit formula for the supremum of copulas with a given curvilinear section and characterizes when this supremum is a copula.
Findings
Explicit formula for the pointwise supremum of copulas.
Characterization of when the supremum is a copula.
Conditions for the supremum to coincide with the greatest quasi-copula.
Abstract
Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also characterize the coincidence of the pointwise supremum and the greatest quasi-copula with the same curvilinear section.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical Approximation and Integration · Financial Risk and Volatility Modeling