Compatibility and attainability of matrices of correlation-based measures of concordance
Hofert, Marius
text
periodical
esp
20190902
continuing
spa
Measures of concordance have been widely used in insurance and risk management to summarize nonlinear dependence among risks modeled by random variables, which Pearson's correlation coefficient cannot capture. However, popular measures of concordance, such as Spearman's rho and Blomqvist's beta, appear as classical correlations of transformed random variables. We characterize a whole class of such concordance measures arising from correlations of transformed random variables, which includes Spearman's rho, Blomqvist's beta and van der Waerden's coefficient as special cases. Compatibility and attainability of square matrices with entries given by such measures are studiedthat is, whether a given square matrix of such measures of concordance can be realized for some random vector and how such a random vector can be constructed. Compatibility and attainability of block matrices and hierarchical matrices are also studied due to their practical importance in insurance and risk management. In particular, a subclass of attainable block Spearman's rho matrices is proposed to compensate for the drawback that Spearman's rho matrices are in general not attainable for dimensions larger than three. Another result concerns a novel analytical form of the Cholesky factor of block matrices which allows one, for example, to construct random vectors with given block matrices of van der Waerden's coefficient.
Marius Hofert, Takaaki Koike
Modelización mediante cópulas
Teoría de matrices
Cálculo actuarial
Matemática del seguro
6
Astin bulletin
Belgium : ASTIN and AFIR Sections of the International Actuarial Association
0515-0361
MAP20077000420
02/09/2019 Volumen 49 Número 3 - septiembre 2019 , p. 885-918
MAP
191106
20191106164120.0
MAP20190032162
spa