  Under the Basel II standards, the Operational Risk (OpRisk) advanced
measurement approach is not prescriptive regarding the class of statistical
model utilised to undertake capital estimation. It has however become well
accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the
individual OpRisk loss process corresponding to the Basel II Business
line/event type. In this paper we derive a novel class of doubly stochastic
alpha-stable family LDA models. These models provide the ability to capture the
heavy tailed loss process typical of OpRisk whilst also providing analytic
expressions for the compound process annual loss density and distributions as
well as the aggregated compound process annual loss models. In particular we
develop models of the annual loss process in two scenarios. The first scenario
considers the loss process with a stochastic intensity parameter, resulting in
an inhomogeneous compound Poisson processes annually. The resulting arrival
process of losses under such a model will have independent counts over
increments within the year. The second scenario considers discretization of the
annual loss process into monthly increments with dependent time increments as
captured by a Binomial process with a stochastic probability of success
changing annually. Each of these models will be coupled under an LDA framework
with heavy-tailed severity models comprised of $\alpha$-stable severities for
the loss amounts per loss event. In this paper we will derive analytic results
for the annual loss distribution density and distribution under each of these
models and study their properties.
