Analysis of an aggregate loss model in a Markov renewal regime Articles uri icon

publication date

  • May 2021

start page

  • 1

end page

  • 20


  • 125869


  • 396

International Standard Serial Number (ISSN)

  • 0096-3003

Electronic International Standard Serial Number (EISSN)

  • 1873-5649


  • 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 (MAP2), 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 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-loss times distribution leads to higher capital charges.


  • Mathematics
  • Statistics


  • batch markovian arrival process; dependent loss times; double-pareto lognormal distribution; loss modeling; markov renewal theory; mle estimation; operational risk; overdispersion; ph distribution; value-at-risk