Publication: Two maxentropic approaches to determine the probability density of compound risk losses

 dc.affiliation.dpto UC3M. Departamento de EconomÃ­a de la Empresa es dc.contributor.author GonÃ§alves Pereira, Erika Patricia dc.contributor.author Gzyl Buchholz, Henryk dc.contributor.author Mayoral, Silvia dc.date.accessioned 2022-06-01T15:26:30Z dc.date.available 2022-06-01T15:26:30Z dc.date.issued 2015-05-01 dc.description.abstract Here we present an application of two maxentropic procedures to determine the probability density distribution of a compound random variable describing aggregate risk, using only a finite number of empirically determined fractional moments. The two methods that we use are the Standard method of Maximum Entropy (SME) and the method of Maximum Entropy in the Mean (MEM). We analyze the performance and robustness of these two procedures in several numerical examples, in which the frequency of losses is Poisson and the individual losses are lognormal random variables. We shall verify that the reconstructions obtained pass a variety of statistical quality criteria, and provide good estimations of VaR and TVaR, which are important measures for risk management purposes. As side product of the work, we obtain a rather accurate numerical description of the density of such compound random variable. These approaches are also used to develop a procedure to determine the distribution of the individual losses from the knowledge of the total loss. Thus, if the only information available is the total loss, and the nature of the frequency of losses is known, the method of maximum entropy provides an efficient method to determine the individual losses as well en dc.identifier.bibliographicCitation Gomes-GonÃ§alves, E., Gzyl, H., & Mayoral, S. (2015). Two maxentropic approaches to determine the probability density of compound risk losses. Insurance: Mathematics and Economics, 62, pp. 42-53. en dc.identifier.doi https://doi.org/10.1016/j.insmatheco.2015.03.001 dc.identifier.issn 0167-6687 dc.identifier.publicationfirstpage 42 es dc.identifier.publicationlastpage 53 es dc.identifier.publicationtitle INSURANCE MATHEMATICS & ECONOMICS en dc.identifier.publicationvolume 62 es dc.identifier.uri https://hdl.handle.net/10016/34969 dc.identifier.uxxi AR/0000017016 dc.language.iso eng es dc.publisher Elsevier es dc.rights Â© 2015 Elsevier B.V. All rights reserved en dc.rights AtribuciÃ³n-NoComercial-SinDerivadas 3.0 EspaÃ±a * dc.rights.accessRights open access es dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ * dc.subject.eciencia EconomÃ­a es dc.subject.eciencia Empresa es dc.subject.other Total loss distribution en dc.subject.other Maximum entropy methods en dc.subject.other Laplace transform en dc.subject.other Decompounding en dc.title Two maxentropic approaches to determine the probability density of compound risk losses en dc.type research article * dc.type.hasVersion AM * dspace.entity.type Publication
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