The benchmark theory of mathematical finance is the Black-Scholes-Merton theory, based on Brownian motion as the driving noise process for stock prices. Here the distributions of financial returns of the stocks in a portfolio are multivariate normal. The two most obvious limitations here concern symmetry and thin tails, neither being consistent with real data. The most common replacement for the multinormal is parametric, the Barndorff-Nielsen generalized hyperbolic family. Here we advocate the use of semi-parametric models. A generalisation of the hyperbolic family involves normal variance-mean mixtures. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. Implementation is considered: we present simulation studies, and fit our model to several financial data series, and discuss aspects of risk management.