  In mathematical finance and other applications of stochastic processes, it is
frequently the case that the characteristic function may be known but explicit
forms for density functions are not available. The simulation of any
distribution is greatly facilitated by a knowledge of the quantile function, by
which uniformly distributed samples may be converted to samples of the given
distribution. This article analyzes the calculation of a quantile function
direct from the characteristic function of a probability distribution, without
explicit knowledge of the density. We form a non-linear integro-differential
equation that despite its complexity admits an iterative solution for the power
series of the quantile about the median. We give some examples including tail
models and show how to generate C-code for examples.
