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

Gonçalves Pereira, Erika Patricia; Gzyl Buchholz, Henryk; Mayoral, Silvia

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

dc.affiliation.dpto	UC3M. Departamento de Economía de la Empresa	es
dc.contributor.author	Gonçalves 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-Gonçalves, 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	© 2015 Elsevier B.V. All rights reserved	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	es
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Economía	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