The normal inverted gamma mixture or generalized Student t and the symmetric double Weibull, as well as their logarithmic counterparts, are proposed for modeling some loss distributions in non-life insurance and daily index return distributions in financial markets. For three specific data sets, the overall goodness-offit from these models, as measured simultaneously by the negative log-likelihood, chi-square and minimum distance statistics, is found to be superior to that of various "good" competitive models including the log-normal, the Burr, and the symmetric a-stable distribution. Furthermore, the study justifies on a statistical basis different important models of financial returns like the model of Black-Scholes (1973), the log-Laplace model of Hurlimann (1995), the normal mixture by Praetz (1972), the symmetric a-stable model by Mandelbrot (1963) and Fama (1965), and the recent double Weibull as limiting geometric-multiplication stable scheme in Mittnik and Rachev (1993). As an application, the prediction of one-year index returns from daily index returns is discussed. KEYWORDSClaim size data, financial market data, index return, normal inverted gamma mixture, generalized Student t, symmetric double Weibull, goodness-offit.

An expected utility model of asset choice, which takes into account asset pricing, is considered. The obtained portfolio selection problem under utility pricing is solved under several assumptions including quadratic utility, exponential utility and multivariate symmetric elliptical returns. The obtained unique solution, called optimal utility portfolio, is shown mean-variance efficient in the classical sense. Various questions, including conditions for complete diversification and the behavior of the optimal portfolio under univariate and multivariate ordering of risks as well as riskadjusted performance measurement, are discussed.