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Modeling non-life insurance price for risk without historical information

Publication . Azevedo, Filipe Charters de; Oliveira, Teresa A.; Oliveira, Amilcar

How should an insurer price a risk for which there is no history? This work intends to show, step by step, which main mechanisms are needed to capture the tariff model of another insurance company minimizing the risk involved. The document generally deals with the price-making mechanisms in non-life insurance through the GLM regression models — Generalized Linear Model, more precisely the Poisson, Gamma and Tweedie models. Given the complexity of the application of these models in experimental design, it is studied a simpler way to characterize the rate, namely considering the Box–Cox transformation with SUR — Seemingly Unrelated Regression. An orthogonal experimental design to collect information is also presented as well as an application of these methods in the motor industry considering different companies.

2016-04Journal article

Open access

The presence of distortions in the extended skew : normal distribution

Publication . Seijas-Macias, J. Antonio; Oliveira, Amilcar; Oliveira, Teresa

In the last years, a very interesting topic has arisen and became the research focus not only for many mathematicians and statisticians, as well as for all those interested in modeling issues: The Skew normal distributions’ family that represents a generalization of normal distribution. The first generalization was developed by Azzalini in 1985, which produces the skew-normal distribution, and introduces the existence of skewness into the normal distribution. Later on, the extended skew-normal distribution is defined as a generalization of skew-normal distribution. These distributions are potentially useful for the data that presenting high values of skewness and kurtosis. Applications of this type of distributions are very common in model of economic data, especially when asymmetric models are underlying the data. Definition of this type of distribution is based in four parameters: location, scale, shape and truncation. In this paper, we analyze the evolution of skewness and kurtosis of extended skew-normal distribution as a function of two parameters (shape and truncation). We focus in the value of kurtosis and skewness and the existence of arange of values where tiny modification of the parameters produces large oscillations in the values. The analysis shows that skewness and kurtosis present an instability development for greater values of truncation. Moreover, some values of kurtosis could be erroneous. Packages implemented in software R confirm the existence of a range where value of kurtosis presents a random evolution.

2017-03Conference object

Open access

Satellite meeting ISI-committee on risk analysis and XI Workshop on Statistics, Mathematics and Computation: book of abstracts

Publication . Oliveira, Teresa; Oliveira, Amilcar; Grilo, Luís; Carapau, Fernando; Dias, Cristina; Santos, Carla

This Book includes the abstracts of the talks presented at the 2017 Satellite Meeting ISI-CRA in honour of Professor David Banks, jointly with the 11th Workshop on Statistics, Mathematics and Computation (WSMC11), hosted at the Politechnic Institute of Portalegre and Universidade Aberta. The location of the meeting was at Universidade Aberta in Lisbon and Politechnic Institute of Portalegre in Portalegre.The meeting organizers celebrated the continued success of WSMC12 and the Satellite Meeting of ISI-CRA. The Executive Committee was constituted by: Teresa Oliveira (Portugal), Lidia Filus (USA), Christos Kitsos (Greece) and M. Ivette Gomes (Portugal).

2017-07Conference object

Open access

Item response theory : a first approach

Publication . Nunes, Sandra; Oliveira, Teresa; Oliveira, Amilcar

The Item Response Theory (IRT) has become one of the most popular scoring frameworks for measurement data, frequently used in computerized adaptive testing, cognitively diagnostic assessment and test equating. According to Andrade et al. (2000), IRT can be defined as a set of mathematical models (Item Response Models – IRM) constructed to represent the probability of an individual giving the right answer to an item of a particular test. The number of Item Responsible Models available to measurement analysis has increased considerably in the last fifteen years due to increasing computer power and due to a demand for accuracy and more meaningful inferences grounded in complex data. The developments in modeling with Item Response Theory were related with developments in estimation theory, most remarkably Bayesian estimation with Markov chain Monte Carlo algorithms (Patz & Junker, 1999). The popularity of Item Response Theory has also implied numerous overviews in books and journals, and many connections between IRT and other statistical estimation procedures, such as factor analysis and structural equation modeling, have been made repeatedly (Van der Lindem & Hambleton, 1997). As stated before the Item Response Theory covers a variety of measurement models, ranging from basic one-dimensional models for dichotomously and polytomously scored items and their multidimensional analogues to models that incorporate information about cognitive sub-processes which influence the overall item response process. The aim of this work is to introduce the main concepts associated with one-dimensional models of Item Response Theory, to specify the logistic models with one, two and three parameters, to discuss some properties of these models and to present the main estimation procedures.

2017-07Conference object

Open access