Abstract: Determining aggregate risk capital has become a fundamental
problem in modern Enterprise Risk Management, and the determination process
has been fairly well studied. The consequent exercise of allocating the
aggregate risk capital to constituents has also been given high priority in both
life and general insurance in such contexts as pricing, performance management,
and proprofitability testing. In fact, the allocation exercise has been often
called the primary driver for calculating the aggregate risk capital.
Unfortunately, the allocation problem is, in general, noticeably more involved
than the problem of calculating the aggregate risk capital. In fact, the former
problem is not easy even when a specificc risk measure that induces the
allocation rule has been assumed, let alone when a class of risk measures is
considered. In this talk I will demonstrate that quite often, the problems of
determining and allocating the aggregate risk capital are of a similar complexity.
Remarkably, this turns out to be the case for the entire class of weighted
risk capital allocations, as well as for the risk portfolios having dependence
structures of the popular multiplicative and additive background risk models.