%0 Journal Article 
%A Ramírez Cobo, Josefa
%A Carrizosa, Emilio
%A Lillo, Rosa E.
%T Analysis of an aggregate loss model in a Markov renewal regime
%D 2021
%@ 0096-3003
%U http://hdl.handle.net/10498/30386
%X 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.
%K Loss modeling
%K Dependent losses times
%K {Markov renewal theory; Overdispersion}
%K Batch Markovian arrival process
%K PH distribution
%K double-Pareto Lognormal distribution
%K MLE estimation
%K Operational risk
%K Value-at-Risk
%~ Universidad de Cádiz