Second-order properties of risk concentrations without the condition of asymptotic smoothness

• DOI: 10.1007/s10687-012-0164-z
• Publication Date: 2013-01-19T03:08:23Z
• Authors: Tiantian Mao; Taizhong Hu
• Keywords: Smoothness

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.