  Interacting particle methods are increasingly used to sample from complex and
high-dimensional distributions. These stochastic particle integration
techniques can be interpreted as an universal acceptance-rejection sequential
particle sampler equipped with adaptive and interacting recycling mechanisms.
Practically, the particles evolve randomly around the space independently and
to each particle is associated a positive potential function. Periodically,
particles with high potentials duplicate at the expense of low potential
particle which die. This natural genetic type selection scheme appears in
numerous applications in applied probability, physics, Bayesian statistics,
signal processing, biology, and information engineering. It is the intention of
this paper to introduce them to risk modeling. From a purely mathematical point
of view, these stochastic samplers can be interpreted as Feynman-Kac particle
integration methods. These functional models are natural mathematical
extensions of the traditional change of probability measures, commonly used to
design an importance sampling strategy. In this article, we provide a brief
introduction to the stochastic modeling and the theoretical analysis of these
particle algorithms. Then we conclude with an illustration of a subset of such
methods to resolve important risk measure and capital estimation in risk and
insurance modelling.
