近年隨著油價、物價上漲所導致的通貨膨脹風險，壽險業者以增額型終身壽險來吸引潛在消費者。另外，由於醫療技術的進步，使得死亡率逐年改善，因此將造成保單在設計時可能將遭受到長壽風險的影響。本篇文章的主要目的即探討長壽風險對於保單責任準備金的影響，並以增額型終身壽險作為本文主要分析標的。首先建構死亡率模型(Lee-Carter模型)，用來配適並模擬死亡率，接著探討增額型終身壽險在各保單年度下之現金流量以及責任準備金的提存，進一步再引進不同的死亡率來探討其現金流量分佈情形與責任準備金之提存。本文研究結果發現，在保險公司未採用遞迴方式計算保費時，當繳費期間愈短、複利利率愈高以及投保年齡愈低時，保險公司所面臨之長壽風險愈大，其後在帶入各種不同死亡率模型，發現死亡改善率愈高，保險公司所面臨之長壽風險愈大，而保險公司在提存責任準備金時，並未考慮到死亡改善率的部分，此對保險公司的財務健全將造成隱憂，本文於此部分建議監理機關透過法規(RBC)的制訂，調整準備金提存的係數，以降低長壽風險對保險公司財務之衝擊。 關鍵字：長壽風險、死亡率模型、增額型終身壽險、保單責任準備金、增額準備金、Lee-Carter Model以及RBC制度。 / With the improvement of medical technology, the life expectancy around the world is increasing year by year during the past decade. Therefore, the increasing whole life insurance policy is popular during these years because its benefits are escalating with time and policyholders think they could gain more benefits when they live longer. Like annuity policies, the increasing whole life insurance could also suffer from the longevity risk, which may have enormous impact on the financial statements of insurers. The purpose of this paper is to discuss the impact of longevity risk on reserves, based on increasing whole life insurance policy. First, we construct Lee-Carter model to fit and simulate mortality rate and assume different mortality improvements from the 2002 Taiwan Standard Ordinary Experience Mortality Table (2002TSO) for further comparisons. And then, we construct a simple model to analyze the cash flows of the increasing whole life policies based on the mortality rates we observed. By constructing a simple model and simulation, we find that if the insurance company does not correctly estimate longevity risk, the insurance company will lose money on the increasing whole life policies. In order to mitigate the insufficiency of life insurers for the increasing whole life policies, we try to provide some supervision suggestion from the view of the risk-based capital (RBC) requirements. We calculate the factor of insurance risk (C2) of RBC requirements because this factor represents the surplus needed to provide for excess claims over expected, both from random fluctuations and from inaccurate pricing for future levels of claims. Keywords: longevity risk, increasing whole life insurance policy, Lee-Carter model, risk-based capital (RBC).

Summaries in English and Afrikaans / Wanvoorstelling van wesenlike feite deur omiss/o aan 'n versekeraar kan tot gevolg he dat die versekeringskontrak ongeldig verklaar word ingevolge die gemene reg. In Mutual and Federal Insurance Co Ltd v Oudtshoorn Municipality 1985 (1) SA 419 (A) is beslis dat wesenlikheid bepaal moet word vanuit die oogpunt van die redelike man. In 'n paging om bewys van die wesenlikheid van feite te vermy, het versekeraars vereis dat aansoekers die voorstellings in die kontrak moat waarborg. Dit het tot gevolg gehad dat voorstellings wat in die kontrak gewaarborg is outomaties wesenlik was. Sedert die invoering van artikel 63(3) van die Versekeringswet 27 van 1943 deur die wetgewer gedurende 1969, is die wesenlikheid van voorstellings egter 'n vereiste, selfs waar dit in die kontrak gewaarborg is. Versekeraars sou dus in die toekoms nie agter kontraktuele wanvoorstellings kon skuil nie. Hierdie maatreel het meer beskerming aan die versekerde gebied. In Qilingele v South African Mutual Life Assurance Society 1993 (1) SA 69 (A) is die toets vir wesenlikheid, soos vereis deur artikel 63{3), aangespreek. Dit het die vraag laat ontstaan of daar twee aparte toetse vir wesenlikheid bestaan, naamlik gemeenregtelik en statuter, en of daar een algemene toets bestaan. / Misrepresentation by omissio of material facts to an insurer may lead to an insurance contract being declared invalid in terms of the common law. In Mutual and Federal Insurance v Oudtshoorn Municipality 1985 (1) SA 419 (A) it was decided to determine materiality in the eyes of the reasonable man. To avoid proving materiality of facts, the insurers required proposers to warrant the representations in the contract. This resulted in the facts automatically being material. In 1969 parliament, .however, enacted section 63(3) of the Insurance Act 27 of 1943 whereby materiality of presentations, even where it was warranted in the contract, became a requirement. Therefore insurers could in future not hide behind contractual misrepresentations. This provided more protection to the insured. Qilingele v SA Mutual Life Assurance Society 1993 (1) SA 69 (A) addresses the test for materiality as required by section 63(3). This resulted in the question whether two separate tests for materiality in terms of common law and statute, or only one exists. / Criminal and Procedural Law / LL.M.

Le traitement des difficultés économiques des entreprises était originellement orienté vers leur liquidation en raison de sa conception traditionnellement moraliste puisque la faillite revêtait, alors, un caractère nécessairement fautif. Sous l’impulsion des différentes crises économiques ainsi que du chômage de masse qu’elles ont provoqué, il est apparu au législateur qu’une telle approche de la défaillance économique devait évoluer. C’est ainsi que, depuis plusieurs décennies maintenant, l’accent est mis sur la prévention des difficultés. Dans cette nouvelle donne, le législateur entend s’appuyer sur la caution, personne physique, comme levier d’anticipation. Il exploite ainsi la qualité de débiteur secondaire de celle-ci, en espérant que sa crainte d’être appelée à la suite du dépôt de bilan, l’amènera à orienter le débiteur principal vers les procédures préventives. C’est à cette fin qu’il lui étend, sous certaines conditions, le bénéfice des mesures protectrices édictées en faveur du débiteur principal dans le cadre de telles procédures. Ces mesures traduisent, ce faisant, un régime dérogatoire du cautionnement dans le cadre des procédures collectives lequel devrait inciter les créanciers, qui cherchent avant tout le règlement de leurs créances, à envisager comme garanties d’insolvabilité du débiteur principal d’autres mécanismes dont ce n’est pas pourtant la fonction première. A son tour, la caution, afin de conjurer le risque de contribution définitive pesant sur elle dans le cas où les procédures envisagées n’ont pas permis de solutionner les difficultés économiques du débiteur principal, devra explorer différentes pistes qui lui permettront de diluer ce risque. / The treatment of the economic difficulties of companies was originally oriented towards liquidation because of its traditionally moralistic approach, since bankruptcy was then necessarily faulty. Driven by the various economic crises and mass unemployment that they provoked, it became clear to the legislator that such an approach to economic failure had to evolve.Thus, for several decades now, the emphasis has been on preventing difficulties. In this new context, the legislator intends to rely on the guarantee, a natural person, as a lever of anticipation. It thus exploits the status of secondary debtor of the latter, hoping that its fear of being called after the bankruptcy, will lead it to direct the principal debtor towards the preventive procedures. It is for this purpose that it extends, under certain conditions, the benefit of the protective measures enacted in favor of the principal debtor in the context of such proceedings. In so doing, these measures constitute a derogation from the guarantee in the context of collective proceedings, which should encourage creditors, who seek above all the settlement of their claims, to consider other mechanisms of this type as collateral for the insolvency of the principal debtor is not the primary function. In turn, the guarantor, in order to ward off the risk of a definitive contribution burdening it in the event that the procedures envisaged have not resolved the economic difficulties of the principal debtor, will have to explore different avenues which will allow it to dilute this risk.

[pt] O objetivo deste estudo foi explorar o problema de churn em seguros de vida, no sentido de prever se o cliente irá cancelar o produto nos próximos 6 meses. Atualmente, métodos de machine learning vêm se popularizando para este tipo de análise, tornando-se uma alternativa ao tradicional método de modelagem da probabilidade de cancelamento através da regressão logística. Em geral, um dos desafios encontrados neste tipo de modelagem é que a proporção de clientes que cancelam o serviço é relativamente pequena. Para isso, este estudo recorreu a técnicas de balanceamento para tratar a base naturalmente desbalanceada – técnicas de undersampling, oversampling e diferentes combinações destas duas foram utilizadas e comparadas entre si. As bases foram utilizadas para treinar modelos de Bagging, Random Forest e Boosting, e seus resultados foram comparados entre si e também aos resultados obtidos através do modelo de Regressão Logística. Observamos que a técnica SMOTE-modificado para balanceamento da base, aplicada ao modelo de Bagging, foi a combinação que apresentou melhores resultados dentre as combinações exploradas. / [en] The purpose of this study is to explore the churn problem in life insurance, in the sense of predicting if the client will cancel the product in the next 6 months. Currently, machine learning methods are becoming popular in this type of analysis, turning it into an alternative to the traditional method of modeling the probability of cancellation through logistics regression. In general, one of the challenges found in this type of modelling is that the proportion of clients who cancelled the service is relatively small. For this, the study resorted to balancing techniques to treat the naturally unbalanced base – under-sampling and over-sampling techniques and different combinations of these two were used and compared among each other. The bases were used to train models of Bagging, Random Forest and Boosting, and its results were compared among each other and to the results obtained through the Logistics Regression model. We observed that the modified SMOTE technique to balance the base, applied to the Bagging model, was the combination that presented the best results among the explored combinations.

La présente thèse est composée d’un ensemble de travaux de recherche en économie appliquée qui s’inscrivent dans le champ contemporain de l’économie de l’assurance. La thèse s’interroge sur comment les pays en développement pourraient développer davantage le secteur d’assurance afin de bénéficier des effets sur l’économie domestique. La première partie de la thèse analyse les déterminants macroéconomiques du développement du secteur d’assurance. Premièrement, les résultats montrent que l'augmentation du revenu par habitant conduit à une augmentation des primes d'assurance-vie et l’assurance-vie est un bien de luxe en Afrique Subsaharienne (chapitre 2). On trouve également des preuves que l’impact marginal du revenu dépend de la qualité de l'environnement juridique et politique. Deuxièmement, l’analyse de l’effet des IDE montre que, ceux-ci constituent un facteur clé dans l'augmentation des primes d'assurance non-vie à la fois dans les pays d’Afrique Subsaharienne (ASS) et dans les autres pays en développement (chapitre 3). Troisièmement, les activités d’assurance-vie et bancaire sont substituables en ASS, cependant les résultats indiquent une causalité unidirectionnelle allant du crédit bancaire au secteur privé vers le développement des activités d’assurance-vie (chapitre 4). La deuxième partie de la thèse analyse l’impact du développement du secteur d’assurance sur l’économie des pays en développement. Premièrement, il apparaît que le développement de l'assurance-vie a un effet positif sur la croissance économique dans les pays en développement d'une part et d'autre part, l’effet marginal de l’assurance-vie est influencé par les caractéristiques structurelles des pays (chapitre 5). Les primes d'assurance augmentent de façon significative la valeur des titres négociés sur le marché financier aussi bien avant et après la crise de 2007(chapitre 6). Troisièmement, la thèse a montré qu’il existe une relation à long terme entre le développement de l’assurance non-vie et l’ouverture commerciale et que les primes d'assurance non-vie améliorent l'ouverture au commerce international aussi bien dans les pays en développement que spécifiquement dans les pays à faible et moyen revenu (chapitre 7). / This thesis is composed of a set of research in applied economics that enroll in the contemporary field of economics of insurance. The thesis analyses how developing countries could develop more the insurance sector and benefit from these effects on local economy. The first part explored the determinants of insurance development from a macroeconomic perspective. First, the results show that increase of income per capita leads to an increase in life insurance premiums and that life insurance is a luxury commodity in Sub-Saharan Africa (chapter 2). We also find evidence that the marginal impact of income varies according to the quality of legal and political environment. Second, analysis of effect of the FDI inflows shows that these are a key factor in increase of non-life insurance premiums in countries of Sub-Saharan Africa (SSA) and in other developing countries (chapter 3). In chapter 4, the results highlighted that the activities of life insurance and banking are substitutable in SSA and, however, there is presence of unidirectional causality running from real private credit density to life insurance and insurance density. The second part of the thesis has analysed effect of development of insurance sector on economy in developing countries. First, it appears that the development of life insurance has a positive effect on economic growth on the one hand and on the other hand marginal effect of life insurance is influenced by the structural characteristics of countries (chapter 5). In chapter 6, the results showed that the insurance premiums significantly increase stock market value traded, before as well and after the 2007's economic crisis. Finally, the thesis showed that there is a long term relationship between the development of non-life insurance and trade openness and that non-life insurance premiums improve openness to international trade as well in developing countries than specifically in low and middle income countries (chapter 7).

La loi du 3 décembre 2001 a, incontestablement, réalisé une avancée majeure dans la protection du conjoint survivant en lui reconnaissant une vocation ab intestat en propriété et en lui permettant, le restant de sa vie, de se maintenir dans le logement conjugal. Néanmoins, cette protection se révèle insuffisante pour celui auquel la loi ferme l’option pour l’usufruit légal : le survivant laissé en la présence d’au moins un enfant issu d’une précédente union. L’introduction de cette distinction à l’article 757du Code civil ne permet pas, en effet, de garantir aux veuves et veufs, issus en particulier de familles recomposées, le maintien de leurs conditions d’existence antérieures, ce, d’autant plus que le droit viager au logement ne peut passe cumuler avec le quart légal en propriété. D’où la nécessité pour le futur défunt d’anticiper les conséquences de sa disparition. Le droit patrimonial de la famille offre, à cet égard, toute une panoplie d’instruments juridiques que le législateur du 23 juin 2006 est venu étoffer, notamment par les nouvelles libéralités-partages et les libéralités graduelles et résiduelles. Toutefois, il sera fait appel aux outils les plus classiques issus, pour les uns, du droit des régimes matrimoniaux avec les avantages matrimoniaux, pour les autres, du droit des libéralités avec l’institution contractuelle entre époux. La voie matrimoniale devant, autant que faire se peut, constituer l’essentiel de la protection du conjoint survivant. Enfin, il sera de bonne pratique de compléter ces mesures de prévoyance conjugale par le recours à l’assurance-vie et à la société civile de gestion de portefeuille de valeurs mobilières. / The law dated December 3rd, 2001 realized, undoubtedly, a major step forward in the protection of the surviving spouse since it recognizes for him a legal vocation in property and it allows himself, the rest of his life, to remain in the matrimonial home. Nevertheless, this protection turns out to be insufficient for the one to which the law closes the option for the legal usufruct : the survivor left with at least one child stemming from a previous union. The introduction of this distinction in the article757 of the civil Code does not, indeed, allow to guarantee for the widows and widowers, stemming in particular from blended families, the preservation of their previous conditions of existence, it, especially as the right life annuity in the accommodation cannot accrue with the legal quarter in property. Where from thenecessity for the future deceased to anticipate the consequences of his disappearance. The property right of the family offers, in this respect, a whole outfit of legal instruments which the legislator of June 23rd, 2006 came to enrich, in particular by new liberalities-divisions and the gradual (and residual) liberalities. However, it will be called on to the most classic stemming tools, for some, of the right of the matrimonial systems with the marital advantages, for the others, the right of the liberalities with the contractual institution between spouses. The marital way in front of, as far as possible, to constitute the main part of the protection of the survivor. Finally, it will be considered as good practice to complete these measures of conjugal foresight by the life insurance and the civil society of management of portfolio of securities.

The target of this graduation thesis is to analyze options you have in order to ensure additional financial resources in retirement age. Public pension system is unsustainable. Pension replacement rates by earnings are unsatisfactory. It is necessary to create a financial reserve individualy. From a financial sphere life insurance and additional pension insurance are offered. It is a state contribution which makes them profitable. Also Life cycle fund is an interesting way especialy in long run. From real investment sphere alocation into real estates or small solar power station with state garanties seem to be very convenient. Investment into descendants are disappreciated nowadays, but it is historical tested way of creation added resources in retirement age.

This Master´s thesis deals with the topic of optional saving for retirement. The pension schemes of selected European countries and of the Czech Republic are described. Also the current situation and the problems these schemes are facing are analyzed. The thesis focuses on the forthcoming pension scheme reform in the Czech Republic. Further, the possible ways of the complementary pension scheme pillar financing using saving products are analyzed in detail. The objective of the thesis is to design an expert system for optimal saving product selection according to client´s individual requirements.

Cielom diplomovej prace je vytvorenie expertného systému založeného na modeloch fuzzy logiky v programoch Excel a MATLAB, pomocou ktorého je možné ohodnotiť rôzne dôchodkové fondy a ďalšie finančné produkty. Vzhľadom na prehlbujúcu sa demografickú krízu, práca ponúka návrhy optimálneho investičného mixu pre tri modelové situácie s cieľom dodatočného finančného zabezpečenia počas dôchodkového veku. Práca je spracovaná pre podmienky Slovenskej republiky, podľa súčasnej situácie a platnej legislatívy.

[pt] Com as falências ocorridas nas últimas décadas, no setor de seguros, um movimento surgiu para desenvolver modelos matemáticos capazes de ajudar no gerenciamento do risco, os chamados modelos internos. No Brasil, a SUSEP, seguindo a tendência mundial, exigiu que as empresas, interessadas em atuar no país, utilizassem um modelo interno para risco de subscrição. Com isto, obter um modelo interno tornou-se primordial para as empresas seguradoras no país. O modelo proposto neste trabalho ilustrado para seguro de vida para risco de subscrição se baseia em Cadeias de Markov, no Teorema Central do Limite, parte paramétrica, e na Simulação de Monte Carlo, parte não paramétrica. Em sua estrutura foi considerada a dependência entre titular e dependentes. Uma aplicação a dados reais mascarados foi feita para analisar o modelo. O capital mínimo requerido calculado utilizando o método híbrido foi comparado com o valor obtido utilizando somente o método paramétrico. Em seguida foi feita a análise de sensibilidade do modelo. / [en] The bankruptcies occurred in recent decades in the insurance sector, a movement arose to develop mathematical models capable of assisting in the management of risk, called internal models. In Brazil, the SUSEP, following the worldwide trend, demanded that the companies, interested in working in the country, using an internal model for underwriting risk. Because of this, developing an internal model has become vital for insurance companies in the country. The proposed model in this work illustrated to life insurance for the underwriting risk was based on the Markov chains, on the Central Limit Theorem to the parametric method, and Monte Carlo Simulation to the non-parametric method. In its structure, the dependence between the holder and dependents was considered. An application to masked real data was made to analyze the model. The minimum required capital calculated using the hybrid method was compared with the value obtained using only the parametric method. Then the sensitivities of the model were investigated.