  Risk aggregation is a popular method used to estimate the sum of a collection
of financial assets or events, where each asset or event is modelled as a
random variable. Applications, in the financial services industry, include
insurance, operational risk, stress testing, and sensitivity analysis, but the
problem is widely encountered in many other application domains. This thesis
has contributed two algorithms to perform Bayesian risk aggregation when model
exhibit hybrid dependency and high dimensional inter-dependency. The first
algorithm operates on a subset of the general problem, with an emphasis on
convolution problems, in the presence of continuous and discrete variables (so
called hybrid models) and the second algorithm offer a universal method for
general purpose inference over much wider classes of Bayesian Network models.
