# Risk concentration under second order regular variation

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Risk concentration under second order regular variation. / Das, Bikramjit; Kratz, Marie.

I: Extremes, Vol. 23, 28.06.2020.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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Das, Bikramjit ; Kratz, Marie. / Risk concentration under second order regular variation. I: Extremes. 2020 ; Vol. 23.

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TY - JOUR

T1 - Risk concentration under second order regular variation

AU - Das, Bikramjit

AU - Kratz, Marie

PY - 2020/6/28

Y1 - 2020/6/28

N2 - 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.

AB - 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.

KW - Asymptotic theory

KW - Dependence

KW - Diversification benefit

KW - Heavy tail

KW - Risk concentration

KW - (Multivariate) second order regular variation

KW - Value-at-risk

U2 - 10.1007/s10687-020-00382-3

DO - 10.1007/s10687-020-00382-3

M3 - Article

VL - 23

JO - Extremes

JF - Extremes

SN - 1572-915X

ER -