By using
these tools from stochastic analysis, a Monte Carlo simulation based risk assessment
can mathematically be decomposed into a well-defined sequence of conditional
Monte Carlo simulations together with a subsequent composition of the total risk out
of these conditional simulation results. The latter composition typically consists of a
tree with conditional probabilities to be assessed at the leaves, and nodes which
either add or multiply the probabilities coming from the subbranches of that node.
Within TOPAZ such a tree is referred to as a collision risk tree (Blom et al., 2001,
2003)