Projecto solvência II - Modelação do risco de subscrição numa companhia de seguros não vida

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Matemática e Aplicações - Actuariado, Estatística e Investigação Operacional

Método de Bootstrap e teoria da credibilidade na estimativa das provisões para sinistros

Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações, no ramo Actuariado, Estatística e Investigação Operacional

Provisões para sinistros: estudo do mercado segurador português

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Modelos determinísticos e estocásticos aplicados ao cálculo de provisões para sinistros

A estimação das provisões para sinistros é de extrema importância na atividade de uma seguradora do ramo Não Vida, porque, por um lado, são necessários recursos suficientes para garantir o pagamento de qualquer sinistro que ocorra e, por outro, o excesso de provisões pode condicionar a rentabilidade da companhia. Assim, faz parte do papel do atuário garantir a adequação destas provisões técnicas. Com esse propósito, é habitualmente utilizado o método determinístico Chain Ladder para a estimação das provisões para sinistros. Contudo, de forma a contornar as limitações desta metodologia, recorre-se a modelos estocásticos, como o modelo proposto por Thomas Mack, uma aplicação dos Modelos Lineares Generalizados, a técnica Bootstrap, entre outros. Dos modelos estocásticos é de salientar um dos mais recentemente estudados, Double Chain Ladder, que está diretamente associado ao método Chain Ladder, trazendo algumas vantagens sobre esse último e possibilitando também a aplicação da técnica Bootstrap e uma simples associação ao método Bornhuetter-Ferguson. O objetivo desta dissertação consiste na aplicação e análise destes modelos na estimação de provisões para sinistros no ramo Não Vida.

Using one-year claim development to chose a large claim reserving technique

Mestrado em Ciências Actuariais

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Una aplicación de RExcel para el cálculo de provisiones técnicas con modelo lineal generalizado

Aplicativo de RExcel que realiza cálculo de provisiones técnicas de prestaciones pendientes para el caso en que el modelo lineal generalizado tiene distribución de Poisson (sobredispersa) junto con función de enlace logarítmica y por lo tanto tiene como caso particular el método Chain-Ladder. Contempla el cálculo de reservas por años de origen, por años de calendario y total. Y permite aplicar fórmulas analíticas o distribuciones estimadas mediante bootstrap.

Estimativa de provisões de IBNR utilizando espaço de estados e filtro de Kalman : um caso brasileiro

Esta dissertação pretende discutir a provisão de sinistros do tipo IBNR, bem como qual a melhor forma de estimar estas provisões. Para tanto, serão utilizados dados reais de uma grande seguradora Brasileira para um produto de seguro de um ramo Não Vida. Serão utilizados no cálculo o clássico método Chain Ladder e em contrapartida um modelo de Espaço de Estados e Filtro de Kalman, discutindo as flexibilidades, vantagens e desvantagens de se utilizar tal metodologia.

Modelos em provisão de sinistros

Part of the work of an insurance company is to keep claims reserves, which is known as the technical reserves, in order to mitigate the risk inherent in their activities and comply with the legal obligations. There are several methods for estimate the claims reserves, deterministics and stochastics methods. One of the most used method is the deterministic method Chain Ladder, of simple application. However, the deterministics methods produce only point estimates, for which the stochastics methods have become increasingly popular because they are capable of producing interval estimates, measuring the variability inherent in the technical reserves. In this study the deterministics methods (Grossing Up, Link Ratio and Chain Ladder) and stochastics (Thomas Mack and Bootstrap associated with Overdispersed Poisson model) will be applied to estimate the claims reserves derived from automobile material damage occurred until December 2012. The data used in this research is based on a real database provided by AXA Portugal. The comparison of results obtained by different methods is hereby presented.

Integrable impurity spin ladder systems

Two different types of integrable impurities in a spin ladder system are proposed. The impurities are introduced in such a way that the integrability of the models is not violated. The models are solved exactly with the Bethe ansatz equations as well as the energy eigenvalues obtained. We show for both models that a phase transition between gapped and gapless spin excitations occurs at a critical value of the rung coupling J. In addition, the dependence of the impurities on this phase transition is determined explicitly. In one of the models the spin gap decreases by increasing the impurity strength A. Moreover, for a fixed A, a reduction in the spin gap by increasing the impurity concentration is also observed.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Developing The Ladder To Professionalism

Developing The Ladder To Professionalism by Tom Baum, Manager, Curricula Development Unit and Patricia Reid, Training Advisor, Curricula Development Unit at the Council for Education, Recruitment and Training, State Agency for Hotels, Catering and Tourism in Dublin, Ireland: “Developments are currently in hand to promote increased professionalism in management within the hotel and catering industry in Ireland. The authors discuss the particular responsibility of educational agencies. Recent initiatives to provide a comprehensive and flexible career ladder encompassing craft training, in-service and “second-chance” education, as well as more conventional college-based initial management are reviewed, as are attempts by various industry associations to enhance the professionalism of members.” In this discussion, the authors have primarily devoted their attention to degree gaps in professionalism in the hospitality industry, and the measures that can be taken to mitigate these circumstances. “The hotel, catering, and tourism industry, in common with others involved in the service function, has been relatively slow to adopt modern approaches to management and technology at all levels,” Baum and Reid want you to know. The authors hail from Ireland and point to steps that the industry, in Ireland, is taking to address service problems. “Developments are taking place in Ireland toward professionalism in management in the context of the Irish hotel and catering industry; education and educationally related institutions have taken a role in contributing to the professionalization of work in this area,” say the authors. Baum and Reid point to CERT’s - The State Training Agency for Hotels, Catering and Tourism - involvement in promoting professionalism in the Irish hospitality industry, and provide a comprehensive graph to illustrate CERT’s paths to successful management. Worthy of note is, proprietor management is more common on that side of the Atlantic’, with most properties tending to be smaller than U.S. chain operations. That fact, by no means suggests that management style is indeed complete in the U.K, but it can be said that maybe such style is more congenial. “However, finding the balance between operationalism and the management and development functions seems to underpin perhaps the cardinal problems of professionalism in hotel and catering management in Ireland,” say the authors. “The dichotomy, clearly represented in the management of the industry, is equally evident within the educational and training system and also in the limited influence of associations…” Baum and Reid expand on that issue. The authors do concede that it is difficult to quantify what exactly constitutes good professionalism in the hospitality industry; it is, after all, a fairly subjective concept. They continue by describing some of the degree and sub-degree programs being offered in Ireland.

Weak coupling of acoustic-like phonons and magnon dynamics in incommensurate spin ladder compound Sr14Cu24O41

Intriguing lattice dynamics has been predicted for aperiodic crystals that contain incommensurate substructures. Here we report inelastic neutron scattering measurements of phonon and magnon dispersions in Sr14Cu24O41, which contains incommensurate one-dimensional (1D) chain and two-dimensional (2D) ladder substructures. Two distinct acoustic phonon-like modes, corresponding to the sliding motion of one sublattice against the other, are observed for atomic motions polarized along the incommensurate axis. In the long wavelength limit, it is found that the sliding mode shows a remarkably small energy gap of 1.7-1.9 meV, indicating very weak interactions between the two incommensurate sublattices. The measurements also reveal a gapped and steep linear magnon dispersion of the ladder sublattice. The high group velocity of this magnon branch and weak coupling with acoustic phonons can explain the large magnon thermal conductivity in Sr14Cu24O41 crystals. In addition, the magnon specific heat is determined from the measured total specific heat and phonon density of states, and exhibits a Schottky anomaly due to gapped magnon modes of the spin chains. These findings offer new insights into the phonon and magnon dynamics and thermal transport properties of incommensurate magnetic crystals that contain low-dimensional substructures.

Quantitative Proteomic Analysis Reveals Metabolic Alterations, Calcium Dysregulation, And Increased Expression Of Extracellular Matrix Proteins In Laminin α2 Chain-deficient Muscle.

Congenital muscular dystrophy with laminin α2 chain deficiency (MDC1A) is one of the most severe forms of muscular disease and is characterized by severe muscle weakness and delayed motor milestones. The genetic basis of MDC1A is well known, yet the secondary mechanisms ultimately leading to muscle degeneration and subsequent connective tissue infiltration are not fully understood. In order to obtain new insights into the molecular mechanisms underlying MDC1A, we performed a comparative proteomic analysis of affected muscles (diaphragm and gastrocnemius) from laminin α2 chain-deficient dy(3K)/dy(3K) mice, using multidimensional protein identification technology combined with tandem mass tags. Out of the approximately 700 identified proteins, 113 and 101 proteins, respectively, were differentially expressed in the diseased gastrocnemius and diaphragm muscles compared with normal muscles. A large portion of these proteins are involved in different metabolic processes, bind calcium, or are expressed in the extracellular matrix. Our findings suggest that metabolic alterations and calcium dysregulation could be novel mechanisms that underlie MDC1A and might be targets that should be explored for therapy. Also, detailed knowledge of the composition of fibrotic tissue, rich in extracellular matrix proteins, in laminin α2 chain-deficient muscle might help in the design of future anti-fibrotic treatments. All MS data have been deposited in the ProteomeXchange with identifier PXD000978 (http://proteomecentral.proteomexchange.org/dataset/PXD000978).

Improvement Of The Physical Performance Is Associated With Activation Of No/pgc-1α/mttfa Signaling Pathway And Increased Protein Expressions Of Electron Transport Chain In Gastrocnemius Muscle From Rats Supplemented With L-arginine.

To examine the influence of l-arginine supplementation in combination with physical training on mitochondrial biomarkers from gastrocnemius muscle and its relationship with physical performance. Male Wistar rats were divided into four groups: control sedentary (SD), sedentary supplemented with l-arginine (SDLA), trained (TR) and trained supplemented with l-arginine (TRLA). Supplementation of l-arginine was administered by gavage (62.5mg/ml/day/rat). Physical training consisted of 60min/day, 5days/week, 0% grade, speed of 1.2km/h. The study lasted 8weeks. Skeletal muscle mitochondrial enriched fraction as well as cytoplasmic fractions were obtained for Western blotting and biochemical analyses. Protein expressions of transcriptor coactivator (PGC-1α), transcriptor factors (mtTFA), ATP synthase subunit c, cytochrome oxidase (COXIV), constitutive nitric oxide synthases (eNOS and nNOS), Cu/Zn-superoxide dismutase (SOD) and manganese-SOD (Mn-SOD) were evaluated. We also assessed in plasma: lipid profile, glycemia and malondialdehyde (MDA) levels. The nitrite/nitrate (NOx(-)) levels were measured in both plasma and cytosol fraction of the gastrocnemius muscle. 8-week l-arginine supplementation associated with physical training was effective in promoting greater tolerance to exercise that was accompanied by up-regulation of the protein expressions of mtTFA, PGC-1α, ATP synthase subunit c, COXIV, Cu/Zn-SOD and Mn-SOD. The upstream pathway was associated with improvement of NO bioavailability, but not in NO production since no changes in nNOS or eNOS protein expressions were observed. This combination would be an alternative approach for preventing cardiometabolic diseases given that in overt diseases a profound impairment in the physical performance of the patients is observed.