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Risk concentration under second order regular variation

Das, Bikramjit and Kratz, Marie LU (2020) In Extremes 23.
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... (More)
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. (Less)
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type
Contribution to journal
publication status
published
subject
keywords
Asymptotic theory, Dependence, Diversification benefit, Heavy tail, Risk concentration, (Multivariate) second order regular variation, Value-at-risk
in
Extremes
volume
23
pages
30 pages
publisher
Kluwer
ISSN
1572-915X
DOI
10.1007/s10687-020-00382-3
language
English
LU publication?
yes
id
6c60e3a7-5c5a-4aa4-ba95-bb78b15be125
alternative location
https://rdcu.be/b5iir
date added to LUP
2020-06-30 15:24:55
date last changed
2020-07-01 09:32:51
@article{6c60e3a7-5c5a-4aa4-ba95-bb78b15be125,
  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.},
  author       = {Das, Bikramjit and Kratz, Marie},
  issn         = {1572-915X},
  language     = {eng},
  month        = {06},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Risk concentration under second order regular variation},
  url          = {http://dx.doi.org/10.1007/s10687-020-00382-3},
  doi          = {10.1007/s10687-020-00382-3},
  volume       = {23},
  year         = {2020},
}