Article
Analysis of an aggregate loss model in a Markov renewal regime
Author/s | Ramírez Cobo, Josefa
Carrizosa Priego, Emilio José Lillo Rodríguez, Rosa Elvira |
Department | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Publication Date | 2020-12-22 |
Deposit Date | 2021-04-23 |
Published in |
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Abstract | In this article we consider an aggregate loss model with dependent losses. The loss oc- currence process is governed by a two-state Markovian arrival process ( MAP 2 ), a Markov renewal process that allows for (1) correlated ... In this article we consider an aggregate loss model with dependent losses. The loss oc- currence process is governed by a two-state Markovian arrival process ( MAP 2 ), a Markov renewal process that allows for (1) correlated inter-loss times, (2) non-exponentially dis- tributed 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 MAP 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. |
Citation | Ramírez Cobo, J., Carrizosa Priego, E.J. y Lillo Rodríguez, R.E. (2020). Analysis of an aggregate loss model in a Markov renewal regime. Applied Mathematics and Computation, 396, 125869-1-125869-20. |
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