Introduced in the 1980s, value at risk has been a popular measure of financial risk. However, value at risk suffers from a number of drawbacks as measure of financial risk. An alternative measure referred to as <italic>expected shortfall</italic> was introduced in late 1990s to circumvent these drawbacks. Much...

We study a portfolio selection model based on Kataoka's safety-first criterion (KSF model in short). We assume that the market is complete but without risk-free asset, and that the returns are jointly elliptically distributed. With these assumptions, we provide an explicit analytical optimal...