Risk concentration under second order regular variation

Bikramjit Das; Marie Kratz

doi:10.1007/s10687-020-00382-3

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arXiv · 1704.02609

Risk concentration under second order regular variation

Bikramjit Das·Marie Kratz

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Abstract

Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to study their convergence rates. In this paper, we provide the asymptotic rate of convergence of the measure of risk concentration for a portfolio of heavy-tailed risk factors, when the portfolio admits the so-called second order regular variation property. Moreover, we explore the relationship between multivariate second order regular variation for a vector (e.g., risk factors) and the second order regular variation property for the sum of its components (e.g., the portfolio of risk factors). Results are illustrated with a variety of examples.

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Bikramjit Das, Marie Kratz. 2017-04-09. Risk concentration under second order regular variation. https://doi.org/10.1007/s10687-020-00382-3

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