Multivariate skew-normal distributions with applications in insurance

In this paper, we discuss the skew-normal distribution as an alternative to the classical normal one in the context of both risk measurement and capital allocation. As main risk measure, we consider the tail conditional expectation (TCE). Hence, we investigate an allocation formula based on the TCE, but we also consider Wang's [Wang, S., 2002. A set of new methods and tools for enterprise risk capital management and portfolio optimization. Working paper. SCOR reinsurance company (www.casact.com/pubs/forum/02sforum/02sf043.pdf)] allocation formula.