Second-order expansions of the risk concentration based on CTE

The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order expansions of the risk concentration based on the risk measure of conditional tail expectation for a portfolio of n independent and identically distributed loss random variables. The key tools are the theory of second-order regular variation and the theory of second-order subexponentiality. Some examples are given.