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）支配，这是一种允许以下特征的马尔可夫更新过程：（1）损失间隔时间相关，（2）损失间隔时间非指数分布，（3）损失计数过度离散。我们得到了用于衡量损失发生过程持续性的若干感兴趣的量。基于真实操作风险数据库，通过分别拟合损失间隔时间和损失严重程度来估计聚合损失模型。MAP2通过直接最大化似然函数进行估计，而严重程度则采用厚尾双帕累托对数正态分布建模。与泊松过程的拟合结果相比，考虑损失间隔时间分布中的相依性和过度离散性将导致更高的资本金要求。