Economics - Research Publications
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ItemA Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums(MDPI AG, 2020-02-01)In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.
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ItemOn the Type I multivariate zero-truncated hurdle model with applications in health insurance(Elsevier, 2020-01-01)In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the EM algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations.
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ItemThe Poisson-conjugate Lindley mixture distribution(Taylor & Francis, 2016-05-18)A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model.
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ItemThe distribution of all French communes: A composite parametric approach(Elsevier, 2016-05-15)The distribution of the size of all French settlements (communes) from 1962 to 2012 is examined by means of a three-parameter composite Lognormal–Pareto distribution. This model is based on a Lognormal density up to an unknown threshold value and a Pareto density thereafter. Recent findings have shown that the untruncated settlement size data is in excellent agreement with the Lognormal distribution in the lower and central parts of the empirical distribution, but it follows a power law in the upper tail. For that reason, this probabilistic family, that nests both models, seems appropriate to describe urban agglomeration in France. The outcomes of this paper reveal that for the early periods (1962–1975) the upper quartile of the commune size data adheres closely to a power law distribution, whereas for later periods (2006–2012) most of the city size dynamics is explained by a Lognormal model.
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ItemModeling claims data with composite Stoppa models(Taylor & Francis, 2016)In this paper, a new class of composite model is proposed for modeling actuarial claims data of mixed sizes. The model is developed using the Stoppa distribution and a mode-matching procedure. The use of the Stoppa distribution allows for more flexibility over the thickness of the tail, and the mode-matching procedure gives a simple derivation of the model compositing with a variety of distributions. In particular, the Weibull–Stoppa and the Lognormal–Stoppa distributions are investigated. Their performance is compared with existing composite models in the context of the well-known Danish fire insurance data-set. The results suggest the composite Weibull–Stoppa model outperforms the existing composite models in all seven goodness-of-fit measures considered.