Risk concentration under second order regular variation

Research output: Contribution to journalArticle


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.


  • Bikramjit Das
  • Marie Kratz
External organisations
  • Singapore University of Technology and Design
  • ESSEC Business School
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Business Administration


  • Asymptotic theory, Dependence, Diversification benefit, Heavy tail, Risk concentration, (Multivariate) second order regular variation, Value-at-risk
Original languageEnglish
Number of pages30
Publication statusPublished - 2020 Jun 28
Publication categoryResearch