Abstract
For the purpose of risk management, the quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. Consider a portfolio of n independent and identically distributed loss random variables with a common survival function \(\overline {F}\) possessing the property of second-order regular variation. Under the additional assumption that \(\overline {F}\) is asymptotically smooth, Degen et al. (Insur Math Econ 46:541–546, 2010) and Mao et al. (Insur Math Econ 51:449–456, 2012) derived second-order approximations of the risk concentrations based on the risk measures of Value-at-Risk and conditional tail expectation, respectively. In this paper, we remove the assumption of the asymptotic smoothness, and reestablish the second-order approximations of these two risk concentrations.
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Mao, T., Hu, T. Second-order properties of risk concentrations without the condition of asymptotic smoothness. Extremes 16, 383–405 (2013). https://doi.org/10.1007/s10687-012-0164-z
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DOI: https://doi.org/10.1007/s10687-012-0164-z
Keywords
- Asymptotic smoothness
- Conditional tail expectation
- Diversification benefit
- Regular variation
- Second-order approximation
- Second-order regular variation
- Value-at-risk