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 ($MA{P}_2$), 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 $MA{P}_2$ 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.

在本文中，我们考虑具有相关损失的总损失模型。损失发生过程受两态马尔可夫到达过程（$\mathrm{中号}\mathrm{一种}{P}_2$）是一个马尔可夫续订过程，它允许（1）相关的互损时间，（2）非指数分布的互损时间以及（3）过度分散的损失计数。获得了一些用于衡量损失发生过程中持久性的兴趣量。给定真实的OpRisk数据库，可通过分别拟合损失间的时间和严重性来估算总损失模型。的$\mathrm{中号}\mathrm{一种}{P}_2$可以通过似然函数的直接最大化来估计，而严重程度可以通过重尾双Double Pareto对数正态分布来建模。与泊松过程提供的拟合相比，结果指出，考虑到损失间时间分布的依赖性和过度分散会导致较高的资本费用。