# CHAPTER 11Modelling Dependencies between Sources of Risk

In this chapter, we concern ourselves with forms of dependency that specifically relate to risk modelling, in contrast to the general dependency relationships that were discussed in Chapter 7. In particular, we refer to cases where the distribution functions (or their sampling) are affected by the dependency; these fall into two main categories:

• Parameter dependencies. These are where the parameters of a distribution are determined from the samples of other distributions (either directly or through other calculations). Thus, the parameters may change at each iteration (recalculation) of the simulation. This type of relationship has a directionality of calculation (and hence an implied causality) inherent in it.
• Sampling dependencies. These are where the sampling of one distribution over the course of a simulation is aligned with the sampling of another. These relationships are of a joint nature, rather than a directional or causal one.

These are discussed in the remainder of this chapter in detail.

## 11.1 Parameter Dependency and Partial Causality

There are cases where one may wish to determine the parameters of a distribution at each iteration (recalculation) of a simulation; such parameters therefore depend (directly or indirectly) on samples of other distributions. A distribution whose parameters are determined in this way can be considered to be a dependent distribution, whereas a distribution with fixed parameters ...

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