[pt] Métodos da teoria de martingais tem sido amplamente utilizados em matemática nos últimos decênios. Mais recentemente, eles também vêm sendo usados em matemática atuarial. Nesta tese discutimos um exemplo de aplicação desta metodologia na demonstração do teorema clássico de Cramér-Lundberg para o problema da ruína. / [en] In the last decades martingale theory tools have been extensively in mathematical finance. More recently, they have also been used in actuarial mathematics. In this thesis we illustrate this methodology in the proof of the classical Lundberg-Crámer theorem for the ruin problem.

This study examines the nature and outcomes of the professional commitment of actuaries. The affective and continuance levels of professional commitment among actuaries are high. Overall, actuaries are more committed to their profession than to their employing organisations. Actuaries who have a high affective commitment to their profession and/or professional association are likely to have become involved in their profession recently and intend to remain in the profession for the foreseeable future. The overall professional-organisational conflict level for actuaries is very low. The outcomes of an increased professional organisational conflict are seen in an increased intention to leave the profession and/or professional association. Findings of this study have implications for the actuarial profession, employers of actuaries and the actuarial professional associations.

Ett mycket debatterat ämne är pensionsområdet. IASB har genom IAS19 gjort ett försök att harmonisera redovisningen inom detta område, trots detta uppkommer det nationella så väl som internationella skillnader. Det huvudsakliga problemet för bolag är att framställa en rättvis diskonteringsränta vid nuvärdesberäkning av deras pensionsskuld. Detta har medfört att de flesta bolag, på grund av kunskapsbrist i ämnet, valt att hyra in denna expertis från en aktuariekonsult. Syftet med denna uppsats är att ur ett beslutsteoretiskt perspektiv beskriva hur aktuariekonsulten resonerar och agerar kring valet avföretags aktuariella antaganden. Det som legat till grund för denna studie är teori och regler utifrån IFRS/IAS 19 samtidigt som valda delar utifrån beslutsteori varit i fokus. För att få svar på vår frågeställning har vi valt att utföra sex intervjuer, fyra med aktuariekonsulter och två med redovisningsansvariga på börsnoterade bolag. Utgångspunkten för ansatsen har tagits från det abduktiva synsättet eftersom en växelverkan mellan teori och empiri genomförts. Denna uppsats har påvisat att konsulterna inte såg sig själva sombeslutsfattare utan intog en mer stöttande roll. Dialogen och förhållningssättet från aktuariekonsult till kund om nödvändig data varen viktig del i beslutsprocessen. Det visade sig även att yrkesheder har en vital betydelse för aktuariekonsulten i deras arbete och i beslutsprocessen. / A much debated topic is the area of pensions. IASB has by IAS 19 made an attempt to harmonize the accounting, although this raises national as well as international differences. The main problem for companies is to produce a fair discount rate in calculating the present value of a pension liability. This has resulted that most companies, due to lack of knowledge on the subject, has decided to hire this expertise from an actuary consultant. The purpose of this paper is within a decision theory perspective, describing how actuary consultant reasons and acts on the choice of corporate actuarial assumptions. To get an answer to our question, we have chosen to perform six interviews, four with actuary consultants and two with the chief accountants for listed companies. The starting point of the approach has been taken by an abductive approach as it is an interaction between theory and empirical implementation. The basis for this study is the theory and rules based on IFRS/IAS 19, while selected parts have been based on decision theory which has been in focus. This thesis has proven the consultants did not see themselves as decisionmakers but took a more supportive role. The data was an important part in the decision process, therefore dialogue and the approach actuary consultants made towards the client played a significant role. This thesis has also shown professional integrity has a vital influence on actuary consultants in their work and in the decision-making process.

[pt] O principal objetivo dessa dissertação é elaborar um modelo estocástico e implementar um simulador para a fluxo de caixa de ativos e passivos para uma simplificação de um plano de previdência privada de um único indivíduo. / [en] The main objective of this work is to propose a sthocastic model and to implement a simulator for the cash flow considering the assets and liabilities of a single person retirement plain.

Este trabalho teve por objetivo geral realizar uma análise de como contabilizar obrigações, com benefícios previdenciários de risco, em regimes de repartição simples, que não preveem formação de reserva ou métodos pré-definidos para isso. Para a consecução de tal objetivo, escolheu-se o benefício de pensão por morte (pensão militar) das Forças Armadascomo objeto de estudo. Nesse sentido, o uso de uma base de dados real contendo as informações individualizadas, pode ser apontado com um dos diferenciais desta pesquisa.Considerando-se o grau de confiabilidade dessa base de dados, além do ineditismo do seu uso em pesquisas acadêmicas, foi possível inferir que os resultados obtidos contribuíram para ratificar diversos conceitos expostos na plataforma teórica. A trajetória metodológica desta pesquisa foi desenvolvida com base no emprego de métodos de custeio atuarial a fim de realizar a projeção de receitas e despesas do sistema de pensões militares. Tais métodos, além da repartição simples, estão alinhados com as abordagens Accumulated Benefit Obligation(ABO) e Projected Benefit Obligation(PBO). Dessa forma, por meio da comparação entre os resultados oriundos das mencionadas abordagens, buscou-se identificar os possíveis impactos nas contas da União, enquanto ente empregador. O confronto de resultados foi realizado com base em uma análise comparativa cujo método principal para o cálculo atuarial foi o fluxo projetado, bem como o fundo financeiro decorrente desse fluxo. Com base nos valores obtidos, diante das diferenças conceituais das abordagens estudadas, entendeu-se que uma forma adequada para permitir a comparação dos resultados seria o cálculo do fundo financeiro futuro a cada período de tempo (t). A análise dos resultados indicou a ocorrência de diferenças representativas entre as abordagens. Na verdade, constatou-se que por não considerar o aumento salarial, o modelo ABO previu menores valores de obrigações com os benefícios futuros, portanto, os valores presentes do fundo financeiro foram maiores do que os modelos que consideraram aumento salarial.Nessa perspectiva, sob o enfoque do ente empregador, os resultados pareceram mais otimistas.Por fim, a abordagem PBO apresentou resultados que pareceram mais aderentes `a realidade do sistema, aproximando-se relativamente do resultado da repartição, no cenário com taxa de juros de 3% (menor taxa utilizada nas projeções). Considerando-se o tempo total das projeções, foi possível observar que, para os modelos de repartição e PBO, existiu um passivo a ser registrado nas contas da União. No entanto, o modelo ABO indicou o contrário, sugerindo que há uma ativo a ser contabilizado no Balanço Geral da União. Tal situação indicou que há diferenças concretas nos resultados, que podem levar os usuários da informação contábil a tomar decisões equivocadas em decorrência dessa distorção de valores. Ficou evidenciado que quanto maior for o horizonte de tempo projetado, maiores serão as diferenças. Ou seja, no menor horizonte adotado (25 anos) constatou-se as menores diferenças. Nesse horizonte, todos os modelos apresentaram valores de que sugerem a existência de um ativo a ser contabilizado. À luz de tal constatação parece razoável sugerir como adequada a revisão do tempo de projeção hoje empregado no âmbito da União (75 anos) na tentativa de reduzir a parcela de incerteza embutida nesse horizonte de longo prazo. / The main objective of this study was to analyze how to account for obligations with risk pension benefits in simple distribution systems that do not provide for reserve formation or predefined methods for this. In order to achieve this objective, the death benefit (military pension) benefit of the Armed Forces was chosen as the object of study. In this sense, the use of a real database containing the individualized information can be pointed out with one of the differentials of this research. Considering the degree of reliability of this database, in addition to the novelty of its use in academic research, it was possible to infer that the results obtained contributed to ratify several concepts exposed in the theoretical platform. The methodological trajectory of this research was developed based on the use of actuarial costing methods in order to realize the projection of revenues and expenses of the military pension system. Such methods, in addition to simple partitioning, are in line with the Accumulated Benefit Obligation (ABO) and Projected Benefit Obligation (PBO) approaches. Thus, through a comparison of the results from the mentioned approaches, it was sought to identify the possible impacts on the Union accounts, as an employer. The comparison of results was performed based on a comparative analysis whose main method for the actuarial calculation was the projected flow, as well as the financial fund resulting from this flow. Based on the values obtained, in view of the conceptual differences of the approaches studied, it was understood that an adequate way to allow the comparison of the results would be the calculation of the future financial fund at each time period (t). The analysis of the results indicated the occurrence of representative differences between the approaches. In fact, it was found that the ABO model predicted lower bond values with future benefits, therefore, the present values of the financial fund were higher than the models that considered a salary increase. From this perspective, under the focus of the employer, the results seemed more optimistic. Finally, the PBO approach presented results that seemed to be more consistent with the reality of the system, relatively close to the result of the distribution, in the scenario with an interest rate of 3 % (lower rate used in the projections). Considering the total projection time, it was possible to observe that, for the allocation models and PBOs, there was a liability to be recorded in the Union accounts. However, the ABO model indicated the opposite, suggesting that there is an asset to be recorded in the Federal Government Balance Sheet. This situation indicated that there are concrete differences in results, which may lead the users of the accounting information to make mistaken decisions as a result of this distortion of values. It has been shown that the larger the projected time horizon, the greater the differences. That is, in the lowest adopted horizon (25 years) the smallest differences were observed. Within this horizon, all models presented values that suggest the existence of an asset to be accounted for. In light of this, it seems reasonable to suggest as appropriate the review of the projection time currently used in the Union (75 years) in an attempt to reduce the uncertainty embedded in this long-term horizon.

Este trabalho teve por objetivo geral realizar uma análise de como contabilizar obrigações, com benefícios previdenciários de risco, em regimes de repartição simples, que não preveem formação de reserva ou métodos pré-definidos para isso. Para a consecução de tal objetivo, escolheu-se o benefício de pensão por morte (pensão militar) das Forças Armadascomo objeto de estudo. Nesse sentido, o uso de uma base de dados real contendo as informações individualizadas, pode ser apontado com um dos diferenciais desta pesquisa.Considerando-se o grau de confiabilidade dessa base de dados, além do ineditismo do seu uso em pesquisas acadêmicas, foi possível inferir que os resultados obtidos contribuíram para ratificar diversos conceitos expostos na plataforma teórica. A trajetória metodológica desta pesquisa foi desenvolvida com base no emprego de métodos de custeio atuarial a fim de realizar a projeção de receitas e despesas do sistema de pensões militares. Tais métodos, além da repartição simples, estão alinhados com as abordagens Accumulated Benefit Obligation(ABO) e Projected Benefit Obligation(PBO). Dessa forma, por meio da comparação entre os resultados oriundos das mencionadas abordagens, buscou-se identificar os possíveis impactos nas contas da União, enquanto ente empregador. O confronto de resultados foi realizado com base em uma análise comparativa cujo método principal para o cálculo atuarial foi o fluxo projetado, bem como o fundo financeiro decorrente desse fluxo. Com base nos valores obtidos, diante das diferenças conceituais das abordagens estudadas, entendeu-se que uma forma adequada para permitir a comparação dos resultados seria o cálculo do fundo financeiro futuro a cada período de tempo (t). A análise dos resultados indicou a ocorrência de diferenças representativas entre as abordagens. Na verdade, constatou-se que por não considerar o aumento salarial, o modelo ABO previu menores valores de obrigações com os benefícios futuros, portanto, os valores presentes do fundo financeiro foram maiores do que os modelos que consideraram aumento salarial.Nessa perspectiva, sob o enfoque do ente empregador, os resultados pareceram mais otimistas.Por fim, a abordagem PBO apresentou resultados que pareceram mais aderentes `a realidade do sistema, aproximando-se relativamente do resultado da repartição, no cenário com taxa de juros de 3% (menor taxa utilizada nas projeções). Considerando-se o tempo total das projeções, foi possível observar que, para os modelos de repartição e PBO, existiu um passivo a ser registrado nas contas da União. No entanto, o modelo ABO indicou o contrário, sugerindo que há uma ativo a ser contabilizado no Balanço Geral da União. Tal situação indicou que há diferenças concretas nos resultados, que podem levar os usuários da informação contábil a tomar decisões equivocadas em decorrência dessa distorção de valores. Ficou evidenciado que quanto maior for o horizonte de tempo projetado, maiores serão as diferenças. Ou seja, no menor horizonte adotado (25 anos) constatou-se as menores diferenças. Nesse horizonte, todos os modelos apresentaram valores de que sugerem a existência de um ativo a ser contabilizado. À luz de tal constatação parece razoável sugerir como adequada a revisão do tempo de projeção hoje empregado no âmbito da União (75 anos) na tentativa de reduzir a parcela de incerteza embutida nesse horizonte de longo prazo. / The main objective of this study was to analyze how to account for obligations with risk pension benefits in simple distribution systems that do not provide for reserve formation or predefined methods for this. In order to achieve this objective, the death benefit (military pension) benefit of the Armed Forces was chosen as the object of study. In this sense, the use of a real database containing the individualized information can be pointed out with one of the differentials of this research. Considering the degree of reliability of this database, in addition to the novelty of its use in academic research, it was possible to infer that the results obtained contributed to ratify several concepts exposed in the theoretical platform. The methodological trajectory of this research was developed based on the use of actuarial costing methods in order to realize the projection of revenues and expenses of the military pension system. Such methods, in addition to simple partitioning, are in line with the Accumulated Benefit Obligation (ABO) and Projected Benefit Obligation (PBO) approaches. Thus, through a comparison of the results from the mentioned approaches, it was sought to identify the possible impacts on the Union accounts, as an employer. The comparison of results was performed based on a comparative analysis whose main method for the actuarial calculation was the projected flow, as well as the financial fund resulting from this flow. Based on the values obtained, in view of the conceptual differences of the approaches studied, it was understood that an adequate way to allow the comparison of the results would be the calculation of the future financial fund at each time period (t). The analysis of the results indicated the occurrence of representative differences between the approaches. In fact, it was found that the ABO model predicted lower bond values with future benefits, therefore, the present values of the financial fund were higher than the models that considered a salary increase. From this perspective, under the focus of the employer, the results seemed more optimistic. Finally, the PBO approach presented results that seemed to be more consistent with the reality of the system, relatively close to the result of the distribution, in the scenario with an interest rate of 3 % (lower rate used in the projections). Considering the total projection time, it was possible to observe that, for the allocation models and PBOs, there was a liability to be recorded in the Union accounts. However, the ABO model indicated the opposite, suggesting that there is an asset to be recorded in the Federal Government Balance Sheet. This situation indicated that there are concrete differences in results, which may lead the users of the accounting information to make mistaken decisions as a result of this distortion of values. It has been shown that the larger the projected time horizon, the greater the differences. That is, in the lowest adopted horizon (25 years) the smallest differences were observed. Within this horizon, all models presented values that suggest the existence of an asset to be accounted for. In light of this, it seems reasonable to suggest as appropriate the review of the projection time currently used in the Union (75 years) in an attempt to reduce the uncertainty embedded in this long-term horizon.

[pt] Aumento de eventos climáticos extremos está colocando empresas de seguros em risco, com perdas que chegam a bilhões de dólares. No Sul do Brasil, municípios sofreram perdas devido a eventos climáticos, incluindo um ciclone bomba que causou prejuízos próximos a 2 bilhões de reais. As perdas são em grande parte seguradas, mas avaliar a probabilidade de perdas devido a desastres naturais é difícil devido à dependência intrínseca entre os riscos expostos. Essa dissertação busca estudar ventos extremos na região Sul do Brasil, visando entender como precificar e diluir o risco em áreas de alto impacto. A pesquisa envolve a análise de dados meteorológicos, econômicos, sinistros reportados por seguradoras, prêmios reportados por seguradoras, estrutura populacional, PIB, relevo e outras variáveis relevantes para a pesquisa. O objetivo é estimar cenários de perdas decorrentes de eventos extremos e oferecer informações relevantes para avaliar estratégias de diluição de risco de perdas econômicas. A dissertação mistura distintas áreas, incluindo Economia, Atuária, Ciência de Dados, Estatística e Matemática. / [en] Increasing extreme weather events are putting insurance companies at risk,with losses reaching billions of dollars. In the South of Brazil, municipalities have suffered losses due to climate events, including a bomb cyclone that caused losses of around 2 billion of reais. These losses are largely insured, but evaluating the probability of losses due to natural disasters is difficult due to the intrinsic dependence between exposed risks. This dissertation seeks to study extreme winds in the Southern region of Brazil, aiming to understand how to price and dilute risk in high impact areas. The research involves the analysis of meteorological and economic data, insurance claims reported by insurers, premiums reported by insurers, population structure, GDP, topography, and other relevant variables for the research. The objective is to estimate loss scenarios resulting from extreme events and offer relevant information to evaluate strategies for diluting the risk of economic losses. The dissertation blends distinct areas, including Economics, Actuarial Science, Data Science, Statistics, and Mathematics.

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)

Text in Afrikaans / Dr. J D Vorster het gedurende sy bedieningstyd in die N.G.Kerk [1935-1978] ontwikkel en gegroei tot 'n invloedryke kerkleier. Die faktore en omstanighede wat tot sy vorming bygedra het is die onderwerp van hierdie studie. Die f eit dat hy in die Stormberge gebore en getoe is asook .karaktereienskappe wat hy van sy voorsate geerf het, was belangrike komponente in sy vorming. Boustene soos godsdiens en volksliefde het in sy ouerhuis die grondslag gele vir sy teologiese beskouings wat op universiteit ontwikkel het. Sedert 1935 is hy in die bediening verder gevorm deur pastorale werk, kerklike vergaderings en briefwisselings. Kulturele en politieke betrokkenheid asook gevangenisstraf het horn bekend gemaak en gebrei. 'n Doktorsgraad in die Kerkreg was verder die regte skoling vir die amp va.n Aktuarius - 'n pos wat met soveel deeglikheid uitgevoer is dat hy later as kerkleier erken is met sy verkiesing as Moderator. / During his ministry in the D.R.Church, dr.J D Vorster developed and grew to become an influential church leader. The subject of this study is the factors and circumstances which contributed to his forming. The fact that he was born and bred in the Stormberge as well as the characteristics he inherited from his ancestors were important components in his forming. Building stones such as religion and nationalism in his parents home laid the .foundation of his theological views which developed at university. He was further formed in his ministry through pastoral work, church meetings and correspondence. Cultural and political participation as well as imprisonment made him well-known and tough. His doctorate in church law put him on the right track for the post of Actuary - an off ice which he filled with so much efficiency that his leadership in the church was recognised with his election as Moderator. / Christian Spirituality, Church History and Missiology / Th. M. (Church History)

Text in Afrikaans, abstract in Afrikaans and English / Different methods of calculation of the loss of support of minor children, are investigated. According to one method (A), one first has to establish that the deceased's income was not all absorbed for his/her own maintenance. Only if there is surplus income available, it can be inferred that the deceased contributed towards the maintenance of the minor children and that the children have suffered a loss. According to another method (B) both parents' income are added and then divided between the family members. The minor child's loss of support is an amount which represent his/her share in the deceased's own income - a child automatically suffers a loss according to this method, in the event of death of a parent. Method B ought to be applied, because it is consistent with the reciprocal duty of support between spouses and the duty of spouses to maintain children. / Verskillende metodes om die verlies aan onderhoud van afhanklike kinders te bereken word ondersoek. Volgens een benadering (A) moet eers vasgestel word of die oorledene se inkomste nie alles geabsorbeer is vir sy /haar eie onderhoud nie. Slegs indien daar surplusinkomste was, kan aanvaar word dat die oorledene bygedra het tot die onderhoud van die minderjarige kinders en dat die kinders 'n verlies ly. Volgens die ander benadering (B) word beide ouers se inkomste bymekaar getel en dan tussen die gesinslede verdeel. Elke minderjarige kind se verlies aan onderhoud is 'n bedrag wat sy/haar aandeel in die oorlede ouer se afsonderlike inkomste verteenwoordig - 'n kind ly outomaties volgens hierdie metode 'n verlies. Metode B behoort meestal aanwending te vind, aangesien dit in ooreenstemming is met die wederkerige onderhoudsplig tussen gades en die plig van ouers om hul kinders te onderhou. / Private Law / LL. M. (Law)