The quantification of diversification benefits due to risk aggregation plays
a prominent role in the (regulatory) capital management of large firms within
the financial industry. However, the complexity of today's risk landscape makes
a quantifiable reduction of risk concentration a challenging task. In the
present paper we discuss some of the issues that may arise. The theory of
second-order regular variation and second-order subexponentiality provides the
ideal methodological framework to derive second-order approximations for the
risk concentration and the diversification benefit.