accedaCRIShttps://accedacris.ulpgc.es/jspuiThe accedaCRIS digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 03 Nov 2024 23:31:50 GMT2024-11-03T23:31:50Z50141A new discrete distribution with actuarial applicationshttp://hdl.handle.net/10553/42939Title: A new discrete distribution with actuarial applications
Authors: Gómez Déniz, Emilio; Sarabia, José María; Calderín Ojeda, Enrique
Abstract: A new discrete distribution depending on two parameters, α<1,α≠0 and 0<θ<1, is introduced in this paper. The new distribution is unimodal with a zero vertex and overdispersion (mean larger than the variance) and underdispersion (mean lower than the variance) are encountered depending on the values of its parameters. Besides, an equation for the probability density function of the compound version, when the claim severities are discrete is derived. The particular case obtained when α tends to zero is reduced to the geometric distribution. Thus, the geometric distribution can be considered as a limiting case of the new distribution. After reviewing some of its properties, we investigated the problem of parameter estimation. Expected frequencies were calculated for numerous examples, including short and long tailed count data, providing a very satisfactory fit.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10553/429392011-01-01T00:00:00ZMeasuring sensitivity in a bonus-malus systemhttp://hdl.handle.net/10553/48780Title: Measuring sensitivity in a bonus-malus system
Authors: Gómez, E.; Hernández, A.; Pérez, J. M.; Vázquez-Polo, Francisco José
Abstract: In performing Bayesian analysis of a bonus-malus system (BMS) it is normal to choose a parametric structure, 70(.), in the insurer's portfolio. According to Bayesian sensitivity analysis the structure function can be modelled by specifying a class F of priors instead of a single prior. In this paper, we examine the ranges of the relativities, i.e. delta(pi) = E[lambdapi (lambda\data)/E[lambdapi(lambda)], pi is an element of Gamma. We illustrate our method with data from [Astin Bulletin 10 (3) (1979) 274]. (C) 2002 Elsevier Science B.V. All rights reserved.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10553/487802002-01-01T00:00:00ZUsing the NIG distribution for modelling actuarial datahttp://hdl.handle.net/10553/53038Title: Using the NIG distribution for modelling actuarial data
Authors: Gomez-Deniz, Emilio; Perez, Jose; Vazquez-Polo, F. J.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10553/530382006-01-01T00:00:00ZAn alternative solution to the problem of overcharges in the Bonus-Malus systemshttp://hdl.handle.net/10553/53041Title: An alternative solution to the problem of overcharges in the Bonus-Malus systems
Authors: Perez-Sanchez, JM; Gomez-Deniz, E; Vazquez-Polo, FJ
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10553/530412003-01-01T00:00:00ZBivariate credibility bonus-malus premiums distinguishing between two types of claimshttp://hdl.handle.net/10553/52633Title: Bivariate credibility bonus-malus premiums distinguishing between two types of claims
Authors: Gómez-Déniz, E.
Abstract: We propose a modification of the bonus-malus system of tarification that is commonly applied in automobile insurance. Under the standard system, the premium assigned to each policyholder is based only on the number of claims made. Therefore, a policyholder who has had an accident producing a relatively small amount of loss is penalised to the same extent as one who has had a more costly accident. This outcome would seem to be unfair.Accordingly, we present a statistical model which distinguishes between two different types of claims, incorporating a bivariate distribution based on the assumption of dependence. We also describe a bivariate prior distribution conjugated with respect to the likelihood. This approach produces credibility bonus-malus premiums that satisfy appropriate transition rules. A practical example of its application is presented and the results obtained are compared with those derived from the traditional Poisson-Gamma model in which only the number of claims is taken into account.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10553/526332016-01-01T00:00:00ZA generalization of the credibility theory obtained by using the weighted balanced loss functionhttp://hdl.handle.net/10553/42948Title: A generalization of the credibility theory obtained by using the weighted balanced loss function
Authors: Gómez Déniz, Emilio
Abstract: n this paper an alternative to the usual credibility premium that arises for weighted balanced loss function is considered. This is a generalized loss function which includes as a particular case the weighted quadratic loss function traditionally used in actuarial science. From this function credibility premiums under appropriate likelihood and priors can be derived. By using weighted balanced loss function we obtain, first, generalized credibility premiums that contain as particular cases other credibility premiums in the literature and second, a generalization of the well-known distribution free approach in [Bühlmann, H., 1967. Experience rating and credibility. Astin Bull. 4 (3), 199-207].
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10553/429482008-01-01T00:00:00ZOn the use of posterior regret Gamma-minimax actions to obtain credibility premiumshttp://hdl.handle.net/10553/42953Title: On the use of posterior regret Gamma-minimax actions to obtain credibility premiums
Authors: Gómez Déniz, Emilio; Pérez Sánchez, José María; Vázquez-Polo, Francisco J.
Abstract: Computing premiums in a Bayesian context requires the use of a prior distribution that the unknown risk parameter follows in the heterogeneous portfolio. Following the methodology that an actuary only has vague information about this parameter and therefore is unable to specify a simple prior, we choose a class Γ of priors and compute posterior regret Γ-minimax premiums which can be written, under appropriate likelihoods and priors, as a credibility formula.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10553/429532006-01-01T00:00:00ZThe net Bayes premium with dependence between the risk profileshttp://hdl.handle.net/10553/42947Title: The net Bayes premium with dependence between the risk profiles
Authors: Hernández Bastida, A.; Fernández Sánchez, M. P.; Gómez Déniz, Emilio
Abstract: In Bayesian analysis it is usual to assume that the risk profiles Θ1 and Θ2 associated with the random variables "number of claims" and "amount of a single claim", respectively, are independent. A few studies have addressed a model of this nature assuming some degree of dependence between the two random variables (and most of these studies include copulas). In this paper, we focus on the collective and Bayes net premiums for the aggregate amount of claims under a compound model assuming some degree of dependence between the random variables Θ1 and Θ2. The degree of dependence is modelled using the Sarmanov-Lee family of distributions [Sarmanov, O.V., 1966. Generalized normal correlation and two-dimensional Frechet classes. Doklady (Soviet Mathematics) 168, 596-599 and Ting-Lee, M.L., 1996. Properties and applications of the Sarmanov family of bivariate distributions. Communications Statistics: Theory and Methods 25 (6) 1207-1222], which allows us to study the impact of this assumption on the collective and Bayes net premiums. The results obtained show that a low degree of correlation produces Bayes premiums that are highly sensitive.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10553/429472009-01-01T00:00:00ZA Bayesian dichotomous model with asymmetric link for fraud in insurancehttp://hdl.handle.net/10553/72511Title: A Bayesian dichotomous model with asymmetric link for fraud in insurance
Authors: Bermudez, Ll.; Perez, J. M.; Ayuso, M.; Gómez Déniz, Emilio; Vázquez Polo, Francisco José
Abstract: Standard binary models have been developed to describe the behavior of consumers when they are faced with two choices. The classical logit model presents the feature of the symmetric link function. However, symmetric links do not provide good fits for data where one response is much more frequent than the other (as it happens in the insurance fraud context). In this paper, we use an asymmetric or skewed logit link, proposed by Chen et al. [Chen, M., Dey, D., Shao, Q., 1999. A new skewed link model for dichotomous quantal response data. J. Amer. Statist. Assoc. 94 (448), 1172-1186], to fit a fraud database from the Spanish insurance market. Bayesian analysis of this model is developed by using data augmentation and Gibbs sampling. The results show that the use of an asymmetric link notably improves the percentage of cases that are correctly classified after the model estimation. (C) 2007 Elsevier B.V. All rights reserved.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10553/725112008-01-01T00:00:00ZThe Log-Lindley distribution as an alternative to the beta regression model with applications in insurancehttp://hdl.handle.net/10553/42928Title: The Log-Lindley distribution as an alternative to the beta regression model with applications in insurance
Authors: Gómez Déniz, Emilio; Sordo, Miguel A.; Calderín Ojeda, Enrique
Abstract: In this paper a new probability density function with bounded domain is presented. The new distribution arises from the generalized Lindley distribution proposed by Zakerzadeh and Dolati (2010). This new distribution that depends on two parameters can be considered as an alternative to the classical beta distribution. It presents the advantage of not including any special function in its formulation. After studying its most important properties, some useful results regarding insurance and inventory management applications are obtained. In particular, in insurance, we suggest a special class of distorted premium principles based on this distribution and we compare it with the well-known power dual premium principle. Since the mean of the new distribution can be normalized to give a simple parameter, this new model is appropriate to be used as a regression model when the response is bounded, being therefore an alternative to the beta regression model recently proposed in the statistical literature.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10553/429282014-01-01T00:00:00ZRisk aggregation in multivariate dependent Pareto distributionshttp://hdl.handle.net/10553/42119Title: Risk aggregation in multivariate dependent Pareto distributions
Authors: Sarabia, José María; Gómez-Déniz, Emilio; Prieto, Faustino; Jordá, Vanesa
Abstract: In this paper we obtain closed expressions for the probability distribution function of aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by Arnold (1983, 2015), which is widely used in insurance and risk analysis. We begin with an individual risk model, where the probability density function corresponds to a second kind beta distribution, obtaining the VaR, TVaR and several other tail risk measures. Then, we consider a collective risk model based on dependence, where several general properties are studied. We study in detail some relevant collective models with Poisson, negative binomial and logarithmic distributions as primary distributions. In the collective Pareto–Poisson model, the probability density function is a function of the Kummer confluent hypergeometric function, and the density of the Pareto–negative binomial is a function of the Gauss hypergeometric function. Using data based on one-year vehicle insurance policies taken out in 2004–2005 (Jong and Heller, 2008) we conclude that our collective dependent models outperform other collective models considered in the actuarial literature in terms of AIC and CAIC statistics.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10553/421192016-01-01T00:00:00ZThe Esscher premium principle in risk theory: a Bayesian sensitivity studyhttp://hdl.handle.net/10553/42959Title: The Esscher premium principle in risk theory: a Bayesian sensitivity study
Authors: Gómez Déniz, Emilio; Hernández Bastida, A.; Vázquez Polo, Francisco José
Abstract: In this paper the Esscher premium calculation principle is applied to the non-compound collective model in a robust Bayesian context. We consider that uncertainty with regard to the prior distribution can be represented by the assumption that the unknown prior distribution belongs to a class of distributions Γ and examine the ranges of the Bayesian premium when the priors belong to such a class. The assessment of the influence of the prior is termed sensitivity analysis or robustness analysis.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10553/429591999-01-01T00:00:00ZUnivariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applicationshttp://hdl.handle.net/10553/42949Title: Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications
Authors: Gómez Déniz, Emilio; Sarabia, José María; Calderín Ojeda, Enrique
Abstract: In this paper we propose a new compound negative binomial distribution by mixing the p negative binomial parameter with an inverse Gaussian distribution and where we consider the reparameterization p = exp (- λ). This new formulation provides a tractable model with attractive properties which make it suitable for application not only in the insurance setting but also in other fields where overdispersion is observed. Basic properties of the new distribution are studied. A recurrence for the probabilities of the new distribution and an integral equation for the probability density function of the compound version, when the claim severities are absolutely continuous, are derived. A multivariate version of the new distribution is proposed. For this multivariate version, we provide marginal distributions, the means vector, the covariance matrix and a simple formula for computing multivariate probabilities. Estimation methods are discussed. Finally, examples of application for both univariate and bivariate cases are given.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10553/429492008-01-01T00:00:00ZExact credibility reference Bayesian premiumshttp://hdl.handle.net/10553/114514Title: Exact credibility reference Bayesian premiums
Authors: Gómez Déniz, Emilio; Vázquez Polo, Francisco José
Abstract: In this paper, reference analysis, the tool provided by Berger et al. (2009), is used to obtain reference Bayesian premiums, which can be helpful when the practitioner has insufficient information to elicit a prior distribution. The Bayesian premiums thus obtained are based exclusively on prior distributions built from the model generated and from the available data. This mechanism produces an objective Bayesian inference, which appears to be the same as the robust Γ-minimax inference. In an informational-theoretical sense, the prior distribution used to make the inference is less informative. These Bayesian premiums are expected to approximate those which would have been obtained using proper priors describing a vague initial state of knowledge. Useful credibility expressions are readily derived by taking classes of priors involving restrictions on moments, i.e., restrictions on the collective or prior premium when the weighted squared-error loss function is used.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10553/1145142022-01-01T00:00:00Z