%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/10498/30594
%X In this article we consider an aggregate loss model with dependent losses. The loss occurrence process is governed by a two-state Markovian arrival process ( M A P 2 ), a Markov renewal process that allows for (1) correlated inter-loss times, (2) non-exponentially distributed inter-loss times and, (3) overdisperse loss counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real OpRisk database, the aggregate loss model is estimated by fitting separately the inter-loss times and severities. The M A P 2 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-loss times distribution leads to higher capital charges.
%K Loss modeling
%K Dependent loss times
%K Markov renewal theory
%K 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