  In this paper we assume a multivariate risk model has been developed for a
portfolio and its capital derived as a homogeneous risk measure. The Euler (or
gradient) principle, then, states that the capital to be allocated to each
component of the portfolio has to be calculated as an expectation conditional
to a rare event, which can be challenging to evaluate in practice. We exploit
the copula-dependence within the portfolio risks to design a Sequential Monte
Carlo Samplers based estimate to the marginal conditional expectations involved
in the problem, showing its efficiency through a series of computational
examples.
