Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Researchers and investors have been attempting to predict stock market activity for years. The possible financial gain that accurate predictions would offer lit a flame of greed and drive that would inspire all kinds of researchers. However, after many of these researchers have failed, they started to hypothesize that a goal such as this is not only improbable, but impossible. Previous predictions were based on historical data of the stock market activity itself and would often incorporate different types of auxiliary data. This auxiliary data ranged as far as imagination allowed in an attempt to find some correlation and some insight into the future, that could in turn lead to the figurative pot of gold. More often than not, the auxiliary data would not prove helpful. However, with the birth of the internet, endless amounts of new sources of auxiliary data presented itself. In this thesis I propose that the near in finite amount of data available on the internet could provide us with information that would improve stock market predictions. With this goal in mind, the different sources of information available on the internet are considered. Previous studies on similar topics presented possible ways in which we can measure internet activity, which might relate to stock market activity. These studies also gave some insights on the advantages and disadvantages of using some of these sources. These considerations are investigated in this thesis. Since a lot of this work is therefore based on the prediction of a time series, it was necessary to choose a prediction algorithm. Previously used linear methods seemed too simple for prediction of stock market activity and a new non-linear method, called Singular Spectrum Analysis, is therefore considered. A detailed study of this algorithm is done to ensure that it is an appropriate prediction methodology to use. Furthermore, since we will be including auxiliary information, multivariate extensions of this algorithm are considered as well. Some of the inaccuracies and inadequacies of these current multivariate extensions are studied and an alternative multivariate technique is proposed and tested. This alternative approach addresses the inadequacies of existing methods. With the appropriate methodology chosen and the appropriate sources of auxiliary information chosen, a concluding chapter is done on whether predictions that includes auxiliary information (obtained from the internet) improve on baseline predictions that are simply based on historical stock market data. / AFRIKAANSE OPSOMMING: Navorsers en beleggers is vir jare al opsoek na maniere om aandeelpryse meer akkuraat te voorspel. Die moontlike finansiële implikasies wat akkurate vooruitskattings kan inhou het 'n vlam van geldgierigheid en dryf wakker gemaak binne navorsers regoor die wêreld. Nadat baie van hierdie navorsers onsuksesvol was, het hulle begin vermoed dat so 'n doel nie net onwaarskynlik is nie, maar onmoontlik. Vorige vooruitskattings was bloot gebaseer op historiese aandeelprys data en sou soms verskillende tipes bykomende data inkorporeer. Die tipes data wat gebruik was het gestrek so ver soos wat die verbeelding toegelaat het, in 'n poging om korrelasie en inligting oor die toekoms te kry wat na die guurlike pot goud sou lei. Navorsers het gereeld gevind dat hierdie verskillende tipes bykomende inligting nie van veel hulp was nie, maar met die geboorte van die internet het 'n oneindige hoeveelheid nuwe bronne van bykomende inligting bekombaar geraak. In hierdie tesis stel ek dus voor dat die data beskikbaar op die internet dalk vir ons kan inligting gee wat verwant is aan toekomstige aandeelpryse. Met hierdie doel in die oog, is die verskillende bronne van inligting op die internet gebestudeer. Vorige studies op verwante werk het sekere spesifieke maniere voorgestel waarop ons internet aktiwiteit kan meet. Hierdie studies het ook insig gegee oor die voordele en die nadele wat sommige bronne inhou. Hierdie oorwegings word ook in hierdie tesis bespreek. Aangesien 'n groot gedeelte van hierdie tesis dus gebasseer word op die vooruitskatting van 'n tydreeks, is dit nodig om 'n toepaslike vooruitskattings algoritme te kies. Baie navorsers het verkies om eenvoudige lineêre metodes te gebruik. Hierdie metodes het egter te eenvoudig voorgekom en 'n relatiewe nuwe nie-lineêre metode (met die naam "Singular Spectrum Analysis") is oorweeg. 'n Deeglike studie van hierdie algoritme is gedoen om te verseker dat die metode van toepassing is op aandeelprys data. Verder, aangesien ons gebruik wou maak van bykomende inligting, is daar ook 'n studie gedoen op huidige multivariaat uitbreidings van hierdie algoritme en die probleme wat dit inhou. 'n Alternatiewe multivariaat metode is toe voorgestel en getoets wat hierdie probleme aanspreek. Met 'n gekose vooruitskattingsmetode en gekose bronne van bykomende data is 'n gevolgtrekkende hoofstuk geskryf oor of vooruitskattings, wat die bykomende internet data inkorporeer, werklik in staat is om te verbeter op die eenvoudige vooruitskattings, wat slegs gebaseer is op die historiese aandeelprys data.

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The main topics of study in this thesis are the Principal Component Analysis (PCA) and Canonical Variate Analysis (CVA) biplots, with the primary focus falling on the quality measures associated with these biplots. A detailed study of different routes along which PCA and CVA can be derived precedes the study of the PCA biplot and CVA biplot respectively. Different perspectives on PCA and CVA highlight different aspects of the theory that underlie PCA and CVA biplots respectively and so contribute to a more solid understanding of these biplots and their interpretation. PCA is studied via the routes followed by Pearson (1901) and Hotelling (1933). CVA is studied from the perspectives of Linear Discriminant Analysis, Canonical Correlation Analysis as well as a two-step approach introduced in Gower et al. (2011). The close relationship between CVA and Multivariate Analysis of Variance (MANOVA) also receives some attention. An explanation of the construction of the PCA biplot is provided subsequent to the study of PCA. Thereafter follows an in depth investigation of quality measures of the PCA biplot as well as the relationships between these quality measures. Specific attention is given to the effect of standardisation on the PCA biplot and its quality measures. Following the study of CVA is an explanation of the construction of the weighted CVA biplot as well as two different unweighted CVA biplots based on the two-step approach to CVA. Specific attention is given to the effect of accounting for group sizes in the construction of the CVA biplot on the representation of the group structure underlying a data set. It was found that larger groups tend to be better separated from other groups in the weighted CVA biplot than in the corresponding unweighted CVA biplots. Similarly it was found that smaller groups tend to be separated to a greater extent from other groups in the unweighted CVA biplots than in the corresponding weighted CVA biplot. A detailed investigation of previously defined quality measures of the CVA biplot follows the study of the CVA biplot. It was found that the accuracy with which the group centroids of larger groups are approximated in the weighted CVA biplot is usually higher than that in the corresponding unweighted CVA biplots. Three new quality measures that assess that accuracy of the Pythagorean distances in the CVA biplot are also defined. These quality measures assess the accuracy of the Pythagorean distances between the group centroids, the Pythagorean distances between the individual samples and the Pythagorean distances between the individual samples and group centroids in the CVA biplot respectively. / AFRIKAANSE OPSOMMING: Die hoofonderwerpe van studie in hierdie tesis is die Hoofkomponent Analise (HKA) bistipping asook die Kanoniese Veranderlike Analise (KVA) bistipping met die primêre fokus op die kwaliteitsmaatstawwe wat daarmee geassosieer word. ’n Gedetailleerde studie van verskillende roetes waarlangs HKA en KVA afgelei kan word, gaan die studie van die HKA en KVA bistippings respektiewelik vooraf. Verskillende perspektiewe op HKA en KVA belig verskillende aspekte van die teorie wat onderliggend is tot die HKA en KVA bistippings respektiewelik en dra sodoende by tot ’n meer breedvoerige begrip van hierdie bistippings en hulle interpretasies. HKA word bestudeer volgens die roetes wat gevolg is deur Pearson (1901) en Hotelling (1933). KVA word bestudeer vanuit die perspektiewe van Linieêre Diskriminantanalise, Kanoniese Korrelasie-analise sowel as ’n twee-stap-benadering soos voorgestel in Gower et al. (2011). Die noue verwantskap tussen KVA en Meerveranderlike Analise van Variansie (MANOVA) kry ook aandag. ’n Verduideliking van die konstruksie van die HKA bistipping word voorsien na afloop van die studie van HKA. Daarna volg ’n indiepte-ondersoek van die HKA bistipping kwaliteitsmaatstawwe sowel as die onderlinge verhoudings tussen hierdie kwaliteitsmaatstawe. Spesifieke aandag word gegee aan die effek van die standaardisasie op die HKA bistipping en sy kwaliteitsmaatstawe. Opvolgend op die studie van KVA is ’n verduideliking van die konstruksie van die geweegde KVA bistipping sowel as twee veskillende ongeweegde KVA bistippings gebaseer op die twee-stap-benadering tot KVA. Spesifieke aandag word gegee aan die effek wat die inagneming van die groepsgroottes in die konstruksie van die KVA bistipping op die voorstelling van die groepstruktuur onderliggend aan ’n datastel het. Daar is gevind dat groter groepe beter geskei is van ander groepe in die geweegde KVA bistipping as in die oorstemmende ongeweegde KVA bistipping. Soortgelyk daaraan is gevind dat kleiner groepe tot ’n groter mate geskei is van ander groepe in die ongeweegde KVA bistipping as in die oorstemmende geweegde KVA bistipping. ’n Gedetailleerde ondersoek van voorheen gedefinieerde kwaliteitsmaatstawe van die KVA bistipping volg op die studie van die KVA bistipping. Daar is gevind dat die akkuraatheid waarmee die groepsgemiddeldes van groter groepe benader word in die geweegde KVA bistipping, gewoonlik hoër is as in die ooreenstemmende ongeweegde KVA bistippings. Drie nuwe kwaliteitsmaatstawe wat die akkuraatheid van die Pythagoras-afstande in die KVA bistipping meet, word gedefinieer. Hierdie kwaliteitsmaatstawe beskryf onderskeidelik die akkuraatheid van die voorstelling van die Pythagoras-afstande tussen die groepsgemiddeldes, die Pythagoras-afstande tussen die individuele observasies en die Pythagoras-afstande tussen die individuele observasies en groepsgemiddeldes in die KVA bistipping.

nÃo hà / O ordenamento jurÃdico brasileiro, à partir de 1998, permitiu que os entes federativos estados e municÃpios pudessem migrar do Regime Geral de PrevidÃncia (RGPS), capitaneado pelo INSS, para um Regime PrÃprio de PrevidÃncia Social (RPPS) tomando o cuidado para os aportes financeiros necessÃrios para a harmonia do equilÃbrio atuarial de modo a garantir, no futuro, o pagamento dos benefÃcios a quem de direito (massa laboral incluÃda nos regimes previdenciÃrios), de sorte que dos 5.509 municÃpios brasileiros, 1.957 instituÃram os seus RPPS e, 55 municÃpios no Estado do CearÃ, dos 184 existentes. O objetivo principal desta pesquisa foi apurar o resultado atuarial dos RPPS instituÃdos nos municÃpios cearenses por meio de um software construÃdo pelo autor e confrontÃ-lo com o resultado atuarial contido nos Demonstrativos de Resultado das AvaliaÃÃes Atuariais â DRRAÂs. De acordo com os cÃlculos realizados os RPPS municipais cearenses apresentam dÃficit atuarial no montante de R$ 3.361.632.976,77, enquanto o valor do resultado atuarial demonstrados nos DRAAÂs apresentam dÃficit atuarial no valor de R$ 10.344.705.187,76. Em ambas as apuraÃÃes o resultado deficitÃrio tem concentraÃÃo nos municÃpios de Fortaleza, CanindÃ, MaracanaÃ, Juazeiro do Norte e Itapipoca. Na 1. e 2. apuraÃÃo os municÃpios de Amontada e Caucaia se mostraram superavitÃrios, acrescentando-se, tambÃm, que os municÃpios de Cruz e Fortim se revelaram superavitÃrios no cÃlculo realizado pelo autor. O dÃficit atuarial do MunicÃpio de Itapipoca apresentou-se preciso, tanto no cÃlculo formulado pelo autor, quanto no demonstrado no DRRA do ente. Conclui-se que os entes previdenciÃrios deficitÃrios nÃo oferecem sistema de estrutura para o acÃmulo de recursos para o pagamento de compromissos definidos nos planos de benefÃcios. / The Brazilian legal system , starting from 1998 revealed that the federative states and municipalities could migrate from the General Provident Fund Scheme ( RGPS ) , headed by the INSS , for its Own Social Security System ( RPPS ) taking care to financial contributions necessary for the harmony of actuarial balance to ensure in the future payment of benefits to those eligible ( work force included in pension schemes ) , so that the 5,509 Brazilian municipalities, 1,957 have instituted their RPPS and 55 towns in State of Cearà , the existing 184 . The main objective of this research was to determine the actuarial results of RPPS established in municipalities of Cearà through a software built by the author and confront him with the actuarial results contained in the statements of income of the Actuarial Reviews - DRRA 's. According to the calculations the Cearà municipal RPPS present actuarial deficit in the amount of R $ 3,361,632,976.77 , while the value of actuarial results demonstrated in the present DRAA 's actuarial deficit of R $ 10,344,705,187.76 . In both calculations the deficit result has concentration in the cities of Fortaleza, CanindÃ, MaracanaÃ, Juazeiro and Itapipoca. In 1. & 2. calculating the municipalities of Amontada and Caucaia proved surplus, also adding to the towns of Cruz and Fortim, the surplus calculation performed by the author. The actuarial deficit of the municipality of Itapipoca presented itself takes both the calculation made by the author, as in shown in the DRRA one. It is concluded that the pension deficit loved not offer structural system for the accumulation of resources for the payment of obligations defined benefit plans. There is evidence that there is no consistency in the figures to the MPAS during transport of the DRAA 's MPAS is recommending the external control bodies investigate that the reason pointed out the differences.

La tesis pretende demostrar que el desarrollo de pensiones complementarias en países emergentes puede ser una fórmula posible de reducción de la pobreza en la vejez, entendida esta como la provisión de elementos suficientes para que el ingreso tras el retiro permita mantenimientos dignos del nivel de vida. Para ello se analiza la viabilidad económica para las empresas y el Estado, y la suficiencia económica para las personas. Concretamente esta tesis investiga acerca del nivel adicional de coste que pueden tener las empresas en el desarrollo de pensiones complementarias que sean suficientes para mantener el nivel de vida. Se determina el incremento en sus costes laborales, también la incidencia que un marco impositivo ad-hoc puede tener para ellas. / The doctoral thesis demonstrates that occupational pension plan development in emerging countries can be a way to prevent poverty in old age, understood as income under retirement would be enough to maintain a minimum standard of living. Thus, the economic feasibility for companies and governments is analyzed. This thesis also deals with level of coverage for population as well. More specifically, research is focused on additional cost for companies to set up occupational pension plans, after designing several models. Labour cost increasing is calculated and put on place comparing among different countries with the benchmarked case study, the Dominican Republic. A tax framework for the country and its companies is proposed and validated, foreseeing the economic flows during the next following 25 years.

Thesis (PhD (Statistics and Actuarial Science))—University of Stellenbosch, 2008. / The problem of variable selection in binary kernel classification is addressed in this thesis. Kernel methods are fairly recent additions to the statistical toolbox, having originated approximately two decades ago in machine learning and artificial intelligence. These methods are growing in popularity and are already frequently applied in regression and classification problems. Variable selection is an important step in many statistical applications. Thereby a better understanding of the problem being investigated is achieved, and subsequent analyses of the data frequently yield more accurate results if irrelevant variables have been eliminated. It is therefore obviously important to investigate aspects of variable selection for kernel methods. Chapter 2 of the thesis is an introduction to the main part presented in Chapters 3 to 6. In Chapter 2 some general background material on kernel methods is firstly provided, along with an introduction to variable selection. Empirical evidence is presented substantiating the claim that variable selection is a worthwhile enterprise in kernel classification problems. Several aspects which complicate variable selection in kernel methods are discussed. An important property of kernel methods is that the original data are effectively transformed before a classification algorithm is applied to it. The space in which the original data reside is called input space, while the transformed data occupy part of a feature space. In Chapter 3 we investigate whether variable selection should be performed in input space or rather in feature space. A new approach to selection, so-called feature-toinput space selection, is also proposed. This approach has the attractive property of combining information generated in feature space with easy interpretation in input space. An empirical study reveals that effective variable selection requires utilisation of at least some information from feature space. Having confirmed in Chapter 3 that variable selection should preferably be done in feature space, the focus in Chapter 4 is on two classes of selecion criteria operating in feature space: criteria which are independent of the specific kernel classification algorithm and criteria which depend on this algorithm. In this regard we concentrate on two kernel classifiers, viz. support vector machines and kernel Fisher discriminant analysis, both of which are described in some detail in Chapter 4. The chapter closes with a simulation study showing that two of the algorithm-independent criteria are very competitive with the more sophisticated algorithm-dependent ones. In Chapter 5 we incorporate a specific strategy for searching through the space of variable subsets into our investigation. Evidence in the literature strongly suggests that backward elimination is preferable to forward selection in this regard, and we therefore focus on recursive feature elimination. Zero- and first-order forms of the new selection criteria proposed earlier in the thesis are presented for use in recursive feature elimination and their properties are investigated in a numerical study. It is found that some of the simpler zeroorder criteria perform better than the more complicated first-order ones. Up to the end of Chapter 5 it is assumed that the number of variables to select is known. We do away with this restriction in Chapter 6 and propose a simple criterion which uses the data to identify this number when a support vector machine is used. The proposed criterion is investigated in a simulation study and compared to cross-validation, which can also be used for this purpose. We find that the proposed criterion performs well. The thesis concludes in Chapter 7 with a summary and several discussions for further research.

It is well known that the general geometric L´evy market models are incomplete, except for the geometric Brownian and the geometric Poissonian, but such a market can be completed by enlarging it with power-jump assets as Corcuera and Nualart [12] did on their paper. With the knowledge that an incomplete market due to jumps can be completed, we look at other cases of incompleteness. We will consider incompleteness due to more sources of randomness than tradable assets, transactions costs and stochastic volatility. We will show that such markets are incomplete and propose a way to complete them. By doing this we show that such markets can be completed. In the case of incompleteness due to more randomness than tradable assets, we will enlarge the market using the market’s underlying quadratic variation assets. By doing this we show that the market can be completed. Looking at a market paying transactional costs, which is also an incomplete market model due to indifference between the buyers and sellers price, we will show that a market paying transactional costs as the one given by, Cvitanic and Karatzas [13] can be completed. Empirical findings have shown that the Black and Scholes assumption of constant volatility is inaccurate (see Tompkins [40] for empirical evidence). Volatility is in some sense stochastic, and is divided into two broad classes. The first class being single-factor models, which have only one source of randomness, and are complete markets models. The other class being the multi-factor models in which other random elements are introduced, hence are an incomplete markets models. In this project we look at some commonly used multi-factor models and attempt to complete one of them. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.

El objetivo central de esta tesis es presentar el método de Lee Carter para la construcción de tablas dinámicas de mortalidad. Si bien es cierto que estas tablas se pueden utilizar en cualquier campo cuyo interés sea estudiar la evolución de la mortalidad en una población, en este trabajo, el desarrollo está orientado al campo actuarial. Por esta razón, en todos los capítulos, siempre que sea posible, se hace mención a conceptos actuariales. Esta tesis está organizada de la siguiente manera, en el primer capítulo se definen las funciones biométricas, las tablas de mortalidad y se realizan describen algunas aplicaciones en el sector actuarial, utilizando la notación correspondiente. Luego, en el segundo capítulo se definen las tablas dinámicas de mortalidad y se describe el método de Lee Carter. Finalmente, en el tercer capítulo, se construyen tablas de mortalidad dinámicas mediante el método de Lee Carter, se calcula la esperanza de vida al nacer y se presentan algunas aplicaciones en el análisis actuarial. Cabe indicar que, para la construcción de las tablas de mortalidad dinámicas mediante el método de Lee Carter se utiliza el paquete demography del lenguaje R.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

The thesis is focused on problems concerning taxing in the insurance industry. Insurance industry is characteristic with specific labels, which involve also taxation. The main subject of the examination is taxation on incomes in connection with insurance. The first part is focused on personal income taxation, especially taxing of insurance benefits. Then the thesis deals with tax concessions of the life insurance. The main theme of the second part is taxing of insurance companies' incomes. From the view of corporate income tax, the main differences are caused by actuarial provisions, so the main attention is paid to them. Both parts include the international comparison.

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.