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.

翻译：本文研究具有相依损失的聚合损失模型。损失发生过程由两状态马尔可夫到达过程（MAP2）刻画，该过程是一种马尔可夫更新过程，能够实现：（1）损失间隔时间相关、（2）损失间隔时间非指数分布，以及（3）损失计数过度分散。本文推导了衡量损失发生过程持久性的若干关键指标。基于真实操作风险数据库，通过分别拟合损失间隔时间与损失严重程度来估计聚合损失模型。MAP2采用似然函数直接最大化方法进行估计，损失严重程度则通过重尾双帕累托对数正态分布建模。与泊松过程拟合结果相比，研究表明考虑损失间隔时间分布的相依性与过度分散特征将导致更高的资本费用。