ABSTRACT
The first question to ask is whether there is any non-randomised way (that is, other than Monte Carlo) to work out the probability distribution of outputs in a risk model. This is a hopeless task in general, as you can see from the following mathematical formulation:
Pf(x) = ° p(x1, x2, … ,xN) dx1dx2 …dxN {all xi such that f(xi) ≤ x}
which just says that the cumulative probability distribution of an output function f of N random variables x1, … xN is found by integrating over parts of the N dimensional space in which f is less than some number. Obvious, but also impossible in general.
