 Analysis of an aggregate loss model in a Markov renewal regimePepa Ramírez-Cobo, Emilio Carrizosa and Rosa E. Lillo Applied Mathematics and Computation, 2021, vol. 396, issue C Abstract: 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. Keywords: Loss modeling; Dependent loss times; Markov renewal theory; Overdispersion; Batch Markovian arrival process; PH distribution; Double-Pareto Lognormal distribution; MLE estimation; Operational risk; Value-at-Risk (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308225 DOI: 10.1016/j.amc.2020.125869 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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