Analysis of an aggregate loss model in a Markov renewal regime
Abstract
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.
Keywords
Cite
@article{arxiv.2401.14553,
title = {Analysis of an aggregate loss model in a Markov renewal regime},
author = {Pepa Ramírez-Cobo and Emilio Carrizosa and Rosa Elvira Lillo},
journal= {arXiv preprint arXiv:2401.14553},
year = {2024}
}