The diploma thesis deals with the risk management in the insurance practice. The thesis is divided into two parts -- the literature review and the empirical part. In the first section are identified risks endangering the insurance company in their business activities. There are described arrangements risks prevention and elimination. There are also given the basic risks quantification methods. The thesis also describes the system of risk management in Solvency II directive. Basic processes, procedures and methods of the risk management in AXA insurance company are described in the empirical section. In addition is performed a quantification of risks of the selected insurer. Based on this quantification of risks and the risk management analysis, there are suggested further methods and arrangements which may lead to improved risk management for selected insurer.

The diploma thesis deals with current issues of risk management in a selected insurance company. The thesis is conceptually divided into two parts the literature recherche and the empirical part. The first section introduces the individual risks and the basic methods of the quantification of the risks which affect the functioning of commercial insurances. A new system of European insurance regulation, Solvency II, is also described. The empirical part of the diploma thesis deals with the risk quantification of the selected insurance company according to the standard and internal model. The thesis is concluded with the evaluation of the risk management in the selected insurance company and of the company preparedness for the regulatory regime Solvency II. Based on this quantification, the recommendations are put forward to improve the risk management of the selected insurer.

Title: Reinsurance optimization using stochastic programming and risk measures Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Martin Branda, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: The diploma thesis deals with an application of a stochastic progra- mming in a reinsurance optimization problem in terms of a present regulatory framework of the insurance companies within the European Union, i.e. Solvency II. In this context, the reinsurance does not only transfer a portion of the risk to the reinsurer but also reduces an amout of required capital. The thesis utilizes certain risk measures and their properties, premium principles and non-linear in- teger programming. In the theoretical part, there are basic terms from Solvency II, reinsurance, risk measures and the comonotonicity of random variables descri- bed and the optimization problem itself is derived. The approach is then applied in the practical part on data of Czech Insurers' Bureau using the GAMS software. Finally, a stability of the solution is tested depending on several parameters. Keywords: reinsurance optimization, stochastic programming, Solvency II, risk measures 1

nÃo hà / InÃmeras tÃm sido as razÃes que trazem o tema do regime da previdÃncia social dos servidores pÃblicos do Cearà a evidÃncia. Existe uma pressÃo da UniÃo para equacionar o dÃficit atuarial deste sistema. NÃo à sà o estado do Cearà que passa por este desafio. Todo o paÃs passa por um perÃodo de reforma a fim de encontrar soluÃÃes para a manutenÃÃo do sistema. A previdÃncia dos servidores afeta grandemente as contas pÃblicas. Atualmente sÃo protegidos por este sistema mais de 100.000 servidores, entre ativos e inativos do Estado. Este trabalho busca preencher uma lacuna existente sobre um detalhamento da situaÃÃo do regime prÃprio de previdÃncia estadual, atravÃs de uma anÃlise da solvÃncia do respectivo sistema previdenciÃrio, utilizando modelos economÃtricos que mensuram sua sustentabilidade, durante o perÃodo de 2003 a 2012. Os resultados mostram que a dÃvida contraÃda pela previdÃncia no estado do Cearà à administrÃvel. / An ongoing and central concern of large parts of the social sciences is that there are certain issues in which establishing a rigorous consensus is imperative, for instance, as concerns social security of civil servants from Cearà state. This concern is especially significant regarding the Federal Government expenditures and its persistent budget deficits. Of course, Cearà government is by no means alone. And there is considerable added complexity in finding solutions to the Federal system as a whole, with regard to the servant security which greatly affects the public debt. Over 100,000 public servants (active and inactive) are currently protected by this system. This work seeks to shed lights on the real social security system from Cearà state, making use of the so-called solvency ratios which will be applied to the system in question. Further, one makes use of econometric models that measure its sustainability taking into account 2003-2012 years. The results demonstrate that the debt incurred by âcearenseâ pension system is technically manageable.

Nos últimos anos, o mercado segurador brasileiro tem apresentado forte expansão, a qual foi impulsionada pela estabilização econômica e o conseqüente aumento do consumo. No entanto, mediante um crescimento acelerado dos prêmios, eventuais desvios nas premissas adotadas na precificação podem expor as seguradoras a riscos pouco suportáveis no longo prazo. Este é um dos componentes do risco de subscrição, sendo o objeto do presente estudo. No âmbito regulatório, frente ao aumento das complexidades dos serviços financeiros e aos escândalos envolvendo grandes corporações, fez-se necessário o Novo Acordo da Basiléia, o qual introduziu metodologias de apuração da necessidade mínima de capital mais sensível a risco, beneficiando instituições melhor administradas na medida em que requer menor alocação de capital. Nessa mesma linha, no mercado segurador dos países membros da União Européia, segue o projeto Solvência II. Acompanhando a tendência mundial, no Brasil, foram promulgadas novas regras de solvência para o mercado segurador, sendo estabelecidas, num primeiro momento, regras de alocação de capital para cobertura do risco de subscrição, sendo os demais tipos de risco a serem tratados na seqüência. É importante esclarecer que, diferentemente do setor bancário, no mercado segurador brasileiro não é permitida a utilização do próprio modelo interno ou dos parâmetros deste para determinação do capital mínimo requerido regulatório, mas apenas a aplicação de fatores mais suavizados para tal fim. Assim, como este não observa o risco mensurado internamente, o capital regulatório passa a representar um potencial custo imposto às seguradoras, o qual pode impactar diretamente na rentabilidade das linhas de negócio. Nesse sentido, o presente estudo buscou investigar, sob a ótica e limitação de usuário externo das demonstrações contábeis, a existência de indícios que levam a supor que a nova regulamentação sobre o capital mínimo para cobertura do risco de subscrição penalizou as seguradoras de menor porte, tendo-se em vista o seu valor em risco para o nível de confiança de 99,5%. Para tanto, foi necessário: (a) apurar o capital mínimo regulatório, seja com ou sem modelo interno, (b) estimar o valor em risco de cada seguradora para o nível de confiança de 99,5% e (c) distinguir as seguradoras por porte, o qual foi determinado pela técnica de Análise de Conglomerados. O maior desafio foi determinar, para cada seguradora, o item (b), o qual consistiu na estimação das distribuições marginais das perdas por categoria de negócio e a agregação dessas pela aplicação da teoria de cópulas. Depois, calculou-se a razão entre (i) a somatória do grau de provisionamento com a alocação do capital regulatório (abordagens com e sem modelo interno) e (ii) o valor em risco ao nível de confiança de 99,5%. Em seguida, aplicou-se o teste de Mann-Whitney para comparar médias em função do porte. A partir da análise desenvolvida, observou-se que modelo regulatório se mostrou mais coerente quando aplicado às seguradoras médias e grandes, tendo-se em vista que apresentou menor dispersão no parâmetro calculado, cuja mediana estava em torno de 1. Ou seja, para essas, tal resultado sugere que o grau de provisionamento juntamente com o capital regulatório retrata, aproximadamente, o nível de confiança de 99,5%, em consonância com o Projeto Solvência II. A dispersão para as seguradoras pequenas é bem maior e a mediana está próximo a 1,5, o que indica que a abordagem regulatória requer em torno de 50% a mais de recursos que o nível de confiança de 99,5% exige. Esse resultado indica uma desvantagem competitiva se comparada às seguradoras de médio e grande porte. Portanto, os resultados dos testes sugerem que as novas regras de alocação de capital para o mercado segurador brasileiro penalizou as seguradoras de menor porte, impactando na rentabilidade, na precificação e na competitividade se comparada às médias e grandes, o que, por sua vez, tende a favorecer a concentração do setor. / In recent years, the Brazilian insurance market has shown strong growth, which was driven by economic stabilization and the consequent increase in consumption. However, on an environment accelerated growth of premiums, any deviations in the pricing assumptions may expose insurers to unbearable risks in the long term. This is one of the components of the underwriting risk which is the object of this study. In a regulatory side, increased complexities of the financial services and scandals involving large corporations resulted in the creation of the New Basel Accord, which introduced new methodologies to analyze the minimum capital required, considering the risk based capital approach, benefiting the better managed institutions as they require less capital allocation. In a similar vein, countries of the European Union follow the Solvency II project for their insurance market. Following the global trend, new solvency rules for the insurance market were approved in Brazil, being established in the first instance, rules of capital allocation to cover the underwriting risk. Other risk types will be addressed later by the government. It is important to clarify that, unlike the banking sector, the Brazilian insurance market is not allowed to use its own internal model or the parameters of this model to determine the minimum regulatory capital required, but only the application softened factors for this purpose. Thus, as it does not observe the risk internally measured, the regulatory capital becomes a potential cost imposed on the insurers, which can impact directly the profitability of the business lines. Therefore, from the point of view and limitation of external user of financial statements, the present study investigated the existence of signs that could lead to suppose that the new regulations on minimum capital to cover the underwriting risk have penalized the smaller insurance companies, when keeping in view their value at risk for the confidence level of 99,5%. To this end, it was necessary: (a) to determine the minimum regulatory capital, either approaches with or without internal model; (b) to estimate the value at risk of each insurer for the confidence level of 99,5%; and (c) to distinguish insurers by size, according to the cluster analysis technique. The biggest challenge was to determine, for each insurer, the item (b), which consisted in the estimation of marginal distributions of losses and aggregation of these by applying the theory of copulas. Then we calculated the ratio of (i) the sum of the degree of provisioning with the allocation of regulatory capital (approaches with and without internal model) and (ii) the value at risk at the level of confidence 99,5%. Next, we applied the Mann-Whitney Test to compare means of the insurers by size. From the developed analysis, it was observed that the regulatory model was more consistent on medium and large insures as they have shown a lower dispersion in the parameter of interest, presenting a median around 1. That is, for them, the result suggests that the level of provisioning along with the regulatory capital has approximately reflected the confidence level of 99,5%, which is in line with the Solvency II project. Small insurers have shown much higher dispersion and their median is close to 1,5. This indicates that the regulatory approach requires around 50% more resources than the confidence level of 99,5% requires. This represents a disadvantaged competition, if compared with large and medium sized companies. Therefore, the test results suggest that the new rules of capital allocation for the Brazilian insurance market has penalized the smaller insurers, impacting their profitability and competitive pricing when compared with the medium and large ones, which, in turn, tend to favor an industry concentration.

A maioria dos estudos aponta que a dÃvida pÃblica brasileira à solvente. Entretanto, a anÃlise dessa questÃo a nÃvel municipal ainda deixa muito a desejar. Os mÃtodos mais recentes para testar essa problemÃtica envolvem a estimaÃÃo da funÃÃo de reaÃÃo fiscal dos governos. Mas como serà que os municÃpios cearenses tÃm se comportado em relaÃÃo à dÃvida pÃblica e ao superÃvit primÃrio? Esse estudo utiliza dados em Painel para estimar a funÃÃo de resposta fiscal para trÃs grupos de dados constituÃdos por municÃpios do Cearà no perÃodo de 2002 a 2008, sendo que o primeiro grupo compreende uma amostra composta de 147 municÃpios sem a diferenciaÃÃo entre os municÃpios mais ricos e mais pobres. Jà o segundo à composto pelos 37 municÃpios mais ricos e o terceiro e o Ãltimo à composto pelos 37 municÃpios mais pobres do Estado. Essa funÃÃo de reaÃÃo serà estimada por trÃs mÃtodos diferentes: MÃnimos Quadrados OrdinÃrios Agrupados (MQOA), modelo de Efeito Fixo (EF) e modelo de Efeito AleatÃrio (EA). Percebeu-se que em todos os modelos estimados a condiÃÃo de solvÃncia da dÃvida pÃblica à satisfeita. / A lot of studies indicate that the Brazilian public debt is solvent. However, the analysis of this issue at the municipal level still leaves much to be desired. The latest methods to test this problem involve the estimation of fiscal reaction function of government. But how can the state of Cearà have behaved in relation to public debt and primary surplus? This study uses panel data to estimate the fiscal response function for three groups of data consisting of municipalities of Cearà in the period 2002 to 2008, with the first group comprises a composite sample of 147 municipalities with no differentiation between the wealthier and poorer. The second is composed of 37 municipalities and the richest third and final group analyzed a sample consisting of the 37 poorest municipalities of the state. This reaction function is estimated by three different methods: OLS Pooled (OLSP), fixed effect model (FE) and random effect model (RE). It was noticed that in all models estimated the condition of solvency of public debt is satisfied.

This master thesis aims to describe problematics of the stochastic modeling of time structures of interest rates with Vasicek, CIR and Hull-White models and the use of these models in valuation of liabilities and time value of options and guaranties in life insurance. In the theoretical part of the thesis there are fundamentals of stochastic calculus, stochastic models of interest rates and introduction to problematics of life insurance defined. Furthermore, the last practical part of the thesis demonstrates impact of particular models on the value of liabilities in relation to clients and on the value of TVOG of real European life insurance Company.

Diplomová práce se zabývá vývojem a současným stavem pravidel kapitálové přiměřenosti se zaměřením na Novou basilejskou kapitálovou dohodu z roku 2004 (Basel II). Vysvětluje problematiku kapitálové přiměřenosti a její úpravu v České republice. Věnuje se Basilejské kapitálové dohodě (Basel I), podrobně rozebírá pravidla Basel II, zabývá se jejich porovnáním a implementací nových pravidel v Evropě, Spojených státech amerických a České republice. Další část popisuje kvantitativní studie dopadů, nedostatky a kritické připomínky zavádění nového konceptu včetně nastínění možných dopadů v budoucnosti. Poslední kapitola se zabývá pravidly Solvency II pro pojišťovny a jejich porovnáním s pravidly Basel II.

Today's globalization leads to a wide range of new developing trends influencing the insurance market. The main one is a variance in the character of risks. The generation of new threats means for insurers to face up a difficultness with an identification of risks and a prediction of future damages. Solutions of a catastrophic impact of damages are hidden in an alternative transfer of risks and a higher level of assurance. The treat of longevity has its own impact, too. Demographic shock caused by a strain of population has turned people in advanced western markets to life-insurance. Mainly, because of a current insufficient set up of pensions systems, people has searched a new possibility how to insure their post-active life. It has enabled a development of life-insurance products focusing on individual clients' needs and providing several components of flexibility and variability. As a next globalization push, I cannot omit concentration and consolidation ongoing nowadays on the insurance market. Rise of giant conglomerates can be seen in the accent of cost reduction, diversification of risks and using enormous financial power. Nevertheless, the main impulse has risen from the still changing clients' needs with the necessity of obtaining complex financial service. Last but not least, I would like to mention the implementation of a regulatory project Solvency II accompanying by IFRS in the field of the insurance market. Their objectives are a reduction of information asymmetry, a higher stability of the insurance market and transparency and comparability of insurers' financial reporting leading to higher clients' protection.

This thesis focuses on the new regulatory regime for the insurance sector called Solvency II. The aim of this thesis is to introduce and explain the structure of the new regime with its advantages and further to provide an overview of the most important problems linked with the draft of the new directive and the implementation itself. The thesis is divided into five parts. The first two parts shortly survey the current situation in the regulation of insurance markets together with the risks typical for the insurance industry. The third part explains the current rules for solvency calculation and the actual reasons for the introduction of the new regime. The fourth part generally describes the Solvency II directive proposal. Finally, the fifth part deals with the expected impact of the new solvency concept on the insurance market as well as the management of insurance companies.