  In this article we consider an aggregate loss model with dependent losses.
The losses occurrence process is governed by a two-state Markovian arrival
process (MAP2), a Markov renewal process process that allows for (1) correlated
inter-losses times, (2) non-exponentially distributed inter-losses times and,
(3) overdisperse losses counts. Some quantities of interest to measure
persistence in the loss occurrence process are obtained. Given a real
operational risk database, the aggregate loss model is estimated by fitting
separately the inter-losses times and severities. The MAP2 is estimated via
direct maximization of the likelihood function, and severities are modeled by
the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the
fit provided by the Poisson process, the results point out that taking into
account the dependence and overdispersion in the inter-losses times
distribution leads to higher capital charges.
