María Dolores Martínez Miranda
University of Granada
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Publication
Featured researches published by María Dolores Martínez Miranda.
Astin Bulletin | 2012
María Dolores Martínez Miranda; Jens Perch Nielsen; Richard Verrall
By adding the information of reported count data to a classical triangle of reserving data, we derive a suprisingly simple method for forecasting IBNR and RBNS claims. A simple relationship between development factors allows to involve and then estimate the reporting and payment delay. Bootstrap methods provide prediction errors and make possible the inference about IBNR and RBNS claims, separately.
Astin Bulletin | 2011
María Dolores Martínez Miranda; Bent Nielsen; Jens Perch Nielsen; Richard Verrall
In this paper we develop a full stochastic cash flow model of outstanding liabilities for the model developed in Verrall, Nielsen and Jessen (2010). This model is based on the simple triangular data available in most non-life insurance companies. By using more data, it is expected that the method will have less volatility than the celebrated chain ladder method. Eventually, our method will lead to lower solvency requirements for those insurance companies that decide to collect counts data and replace their conventional chain ladder method.
Expert Systems With Applications | 2013
María Dolores Martínez Miranda; Jens Perch Nielsen; Stefan Sperlich; Richard Verrall
The single most important number in the accounts of a non-life insurance company is likely to be the estimate of the outlying liabilities. Since non-life insurance is a major part of our financial industry (amounting to up to 5% of BNP in western countries), it is perhaps surprising that mathematical statisticians and experts of operational research (the natural experts of the underlying problem) have left the intellectual work on estimating this number to actuaries. This paper establishes this important problem in a vocabulary accessible to experts of operations research and mathematical statistics and it can be seen as an open invitation to these two important groups of scholars to join this research. The paper introduces a number of new methodologies and approaches to estimating outstanding liabilities in non-life insurance. In particular it reformulates the classical actuarial technique as a histogram type of approach and improves this classical technique by replacing this histogram by a kernel smoother.
Computational Statistics & Data Analysis | 2013
M.L. Pérez; Lena Janys; María Dolores Martínez Miranda; Jens Perch Nielsen
Practical estimation procedures for the local linear estimation of an unrestricted failure rate when more information is available than just time are developed. This extra information could be a covariate and this covariate could be a time series. Time dependent covariates are sometimes called markers, and failure rates are sometimes called hazards, intensities or mortalities. It is shown through simulations and a practical example that the fully local linear estimation procedure exhibits an excellent practical performance. Two different bandwidth selection procedures are developed. One is an adaptation of classical cross-validation, and the other one is indirect cross-validation. The simulation study concludes that classical cross-validation works well on continuous data while indirect cross-validation performs only marginally better. However, cross-validation breaks down in the practical data application to old-age mortality. Indirect cross-validation is thus shown to be superior when selecting a fully feasible estimation method for marker dependent hazard estimation.
Computational Statistics & Data Analysis | 2013
M. Luz Gámiz Pérez; María Dolores Martínez Miranda; Jens Perch Nielsen
Many nonparametric smoothing procedures consider independent identically distributed stochastic variables. There are also many important nonparametric smoothing applications where the data is more complicated. Survival data or filtered data, defined as following Aalens multiplicative hazard model and aggregated versions of this model, are considered. Aalens model based on counting process theory allows multiple left truncations and multiple right censoring to be present in the data. This type of filtering is omnipresent in biostatistical and demographical applications, where people can join a study, leave the study and perhaps join the study again. The estimation methodology is based on a recent class of local linear density estimators. A new stable bandwidth-selector is developed for these estimators. A data application to aggregated national mortality data is provided, where immigrations to and from the country correspond to respectively left truncation and right censoring. The aggregated mortality data study illustrates that the new practical density estimators provide an important extra element in the visual toolbox for understanding survival data.
Scandinavian Actuarial Journal | 2015
María Dolores Martínez Miranda; Jens Perch Nielsen; Richard Verrall; Mario V. Wüthrich
Double chain ladder demonstrated how the classical chain ladder technique can be broken down into separate components. It was shown that under certain model assumptions and via one particular estimation technique, it is possible to interpret the classical chain ladder method as a model of the observed number of counts with a built-in delay function from when a claim is reported until it is paid. In this paper, we investigate the double chain ladder model further and consider the case when other knowledge is available, focusing on two specific types of prior knowledge, namely prior knowledge on the number of zero-claims for each underwriting year and prior knowledge about the relationship between the development of the claim and its mean severity. Both types of prior knowledge readily lend themselves to be included in the double chain ladder framework.
Journal of Multivariate Analysis | 2013
Wenceslao González Manteiga; María José Lombardía; María Dolores Martínez Miranda; Stefan Sperlich
While today linear mixed effects models are frequently used tools in different fields of statistics, in particular for studying data with clusters, longitudinal or multi-level structure, the nonparametric formulation of mixed effects models is still quite recent. In this paper we discuss and compare different nonparametric estimation methods. In this context we introduce a computationally inexpensive bootstrap method, which is used to estimate local mean squared errors, to construct confidence intervals and to find locally optimal smoothing parameters. The theoretical considerations are accompanied by the provision of algorithms and simulation studies of the finite sample behavior of the methods. We show that our confidence intervals have good coverage probabilities, and that our bandwidth selection method succeeds to minimize the mean squared error for the nonparametric function locally.
Journal of The Royal Statistical Society Series A-statistics in Society | 2015
María Dolores Martínez Miranda; Bent Nielsen; Jens Perch Nielsen
Journal of The Royal Statistical Society Series B-statistical Methodology | 2016
María Luz Gámiz; Enno Mammen; María Dolores Martínez Miranda; Jens Perch Nielsen
Insurance Mathematics & Economics | 2015
Enno Mammen; María Dolores Martínez Miranda; Jens Perch Nielsen