<p>Disertacija je posvećena re&scaron;avanju jednačina distributivnosti gde&nbsp;nepoznate funkcije pripadaju nekim poznatim klasama operacija agregacije&nbsp;i primeni dobijenih re&scaron;enja u teoriji korisnosti. Dobijeni rezultati se generalno mogu podeliti u tri grupe. Prvu grupu čine rezultati iz Glave 2 dobijeni re&scaron;avanjem jednačina distributivnosti između GM-operacija agregacije i&nbsp;oslabljenih uninormi, GM-operacija agregacije i oslabljenih nulanormi, kao i&nbsp;GM-operacija agregacije i operacija agregacije bez neutralnog i absorbujućeg&nbsp;elementa. Druga grupa rezultata, takođe iz Glave 2, je dobijena re&scaron;avanjem&nbsp;jednačina uslovne (oslabljene) distributivnosi neprekidne nulanorme u odnosu&nbsp;na neprekidnu t-konormu, i neprekidne nulanonorme u odnosu na uninorme iz&nbsp;<br />klasa U_min &cup;U_max. Treća grupa rezultata (Glava 3) je proistekla iz primene dobijenih rezultata o uslovoj distributivnosti nulanorme u odnosu na t-konormu&nbsp;u teoriji korisnosti.</p> / <p>This dissertation is devoted to solving distributivity equations involving some well-known classes of aggregation operators, and application&nbsp;the obtained results to utility theory. In general, the obtained results can&nbsp;be divided into three groups. The first group are results from Chapter 2 obtained by solving distributivity equations between GM-aggregation operators&nbsp;and relaxed nullnorm, GM-aggregation operators and relaxed uninorms, as&nbsp;well as GM-aggregation operators and aggregation operators without neutral&nbsp;and absorbing element. The second group are results, also from Chapter 2,&nbsp;obtained by solving conditional (relaxed) distributivity of continuous nullnorm with respect to &nbsp;continuous t-conorm, as well as continuous nullnorm&nbsp;with respect to uninorms from the classes U_min &cup; U_max. The third group are&nbsp;results (Chapter 3) arising from the application results on conditional distributivity of nullnorm with respect to t-conorm in utility theory.</p>

La gestion durable des ressources naturelles vivantes est un problème majeur dans un contexte de raréfaction, dû à l'impact de l'homme et à une incertitude omniprésente. Améliorer les outils existant et en développer de nouveaux pour conseiller les gestionnaires sur l'évolution potentielle des ressources naturelles vivantes, selon divers scénarios environnementaux et de gestion, est nécessaire. Cette thèse a pour but de contribuer au développement d'une méthodologie pour l'aide à la décision pour la gestion des ressources naturelles vivantes, tout en prenant en compte les sources d'incertitude majeures. Ce travail est appliqué au cas de la population de saumon atlantique (Salmo salar L.) de la Nivelle (France). Cette population fait l'objet d'un programme de suivi à long terme et cette espèce a été largement étudiée. Cette dernière est menacée mais elle est toujours ciblée par la pêche commerciale et récréative. Elle illustre la dualité entre conservation et exploitation, qui est au coeur de la gestion des ressources naturelles vivantes. Pour gérer une population, il est nécessaire de comprendre sa dynamique et de prédire son évolution sous divers scénarios environnementaux et de gestion. L'approche Bayésienne fournit un cadre cohérent pour quantifier l'incertitude sous ses différentes formes. Les modèles hiérarchiques permettent l'assimilation de sources de données multiples et de faire des inférences et des prédictions sur des grandeurs spatio-temporelles inconnues. Un modèle stochastique d'état Bayésien, i.e. un modèle hiérarchique Bayésien dynamique, est construit pour étudier la dynamique de la population d'intérêt et pour prédire son évolution. La théorie de la décision en univers incertain fournit un cadre pour aider un individu dans ses choix, mais son application reste difficile. En théorie, une fonction d'utilité qui dépend des conséquences des alternatives de gestion reflète les préférences d'un individu unique impliqué dans un problème décisionnel. En pratique, sa construction est malaisée. Premièrement, il estdifficile de définir une valeur pour chaque conséquence. Deuxièmement, il y a généralement plus d'un individu impliqué dans le problème décisionnel. Par conséquent, on obtient une classe de fonctions d'utilité. De par les différents intérêts, souvent conflictuels, que les gestionnaires ont à prendre en compte, la fonction d'utilité est multi variée. Dans cette thèse, une classe de fonctions d'utilité bi-variées est construite. Elle prend en compte l'incertitude concernant la fonction, les variations de préférence entre les acteurs et la dualité d'intérêts exploitation vs conservation. Ensuite, une analyse de la robustesse est réalisée pour étudier si la décision optimale, i.e. l'utilité espérée maximale, varie lorsque la fonction d'utilité varie.La méthodologie développée dans cette thèse s'est avérée possible et fructueuse. Elle fournit un cadre cohérent pour organiser les interactions entre scientifiques, acteurs et gestionnaires pour atteindre une compréhension commune des problèmes de décision dans la gestion des ressources naturelles vivantes. En reconnaissant explicitement la diversité des acteurs, elle permet d'identifier des conflits potentiels et de guider les gestionnaires vers des compromis acceptables. Cependant, elle demande un haut niveau de formation et d'expertise en modélisation et en calcul. Elle implique également un temps d'analyse important. Comment rendre ces exigences compatibles avec le niveau actuel d'expertise et les agendas à court terme des structures de gestion est un challenge principal pour le futur. / The sustainable management of natural living resources is a major issue in a context of increasing scarcity due to human impact and of pervasive uncertainty. Improving existing tools and developing new ones to advise decision makers on the potential evolution of natural living resources, according to various management and environmental scenarios, is requested. This PhD aims at contributing to the development of a methodology for decision making for natural living resources management, while taking into account major sources of uncertainty. This is achieved through the study case of the Atlantic salmon (Salmo salar L.) population ofthe Nivelle River (France). This population is subjected to a long term monitoring program and the species has been extensively studied. Atlantic salmon is a threatened species but still targeted by commercial and recreational fisheries. It illustrates the duality between conservation and exploitation which is at the heart of natural living resource management. To manage a population, it is necessary to understand its dynamics and to predict its evolution under various management and environmental scenarios. The Bayesian approach provides a coherent framework to quantify uncertainty in its different forms. Hierarchical models allow the assimilation of multiple sources of data and to make spatio-temporal inferences and predictions. A Bayesian state space model, i.e. a Bayesian dynamic hierarchical model, is constructed to study the dynamics of the population of interest and topredict its evolution. The decision theory under uncertainty provides a framework to help an individual in its choices, but its application still raises difficulties. In theory, a utility function depending on the consequences of alternative actions reflects the preferences of a single individual involved in a decision problem. In practice, its construction is challenging. Firstly, it is difficult to assign a value for each consequence. Secondly, there is usually more than one individual involved in the decision problem. Consequently, we obtain a set of utility functions. Due to the various and often conflicting interests the decision maker has to take into account, the utility function is multivariate. In this PhD, a set of bivariate utility functions is constructed. It accounts for the uncertainty about the function, the variation of preferences among stakeholders and the dual interests of exploitation vs conservation. Next, a robustness analysis is performed to study if the optimal decision, i.e. associated to the maximum expected utility, varies when the utility function varies. The methodology developed in this PhD proved practicable and fruitful. It provides a coherent framework for organizing the interactions between scientists, stakeholders and decision makers for reaching a common understanding of decision problems in the management of natural living resources. By acknowledging explicitly the diversity among stakeholders, it allows to identify potential conflict and it helps guiding decision makers towards acceptable trade-off actions. However, it requires a high level of training and expertise in modelling and computation. It involves also thoughtful and time consuming analyses. How to render these requirements compatible with the current level of expertise and the short term agendas of management bodies is a main challenge for the near future.

The aim of the diploma thesis is to solve a particular problem via methods and instruments of multi-criteria decision-making under risk -- the choice of a suitable location of a swimming pool in the city of Písek. Every single phase of the decision-making process is described in the theoretical part of the thesis and followed in the practical part. The process was divided into stages: the problem specification, setting objectives, determination of the importance of the criteria, generation of alternatives and identification of their consequences, determination the significance of the risk factors, the probability of their occurrence, setting the impacts of the risk alternatives, evaluation of the alternatives and the choice of the most desirable one, potential threats and opportunities analysis. The theoretical part consists of a review of methods suitable for the given phase. More in-detail focus is put on the methods used in the practical part. To sum up, the diploma thesis provide the reader with the recommendation of the most appropriate location for the construction of the swimming pool. Additionally, it identifies the most important threats and opportunities related to this preference.

En France, la recherche contre le cancer est un enjeu majeur de santé publique. On estime notamment que le nombre de nouveaux cas de cancer a plus que doublé entre 1980 et 2012. L’hétérogénéité des caractéristiques tumorales, pour un même cancer, impose des défis complexes dans la recherche de traitements efficaces. Dans ce contexte, des espoirs importants sont placés dans la recherche de biomarqueurs prédictifs reflétant les caractéristiques des patients ainsi que de leur tumeur afin d’orienter le choix de la stratégie thérapeutique. Par exemple, pour les cancers colorectaux métastatiques, il est maintenant reconnu que l’ajout de cetuximab (un anti-EGFR) à la chimiothérapie classique (ici le FOLFOX4), n’apporte un bénéfice qu’aux patients dont le gène KRAS est non muté. Le gène KRAS est ici un biomarqueur prédictif binaire, mais de nombreux biomarqueurs sont le résultat d’une quantification ou d’un dosage. L’objectif de cette thèse est dans un premier temps, de quantifier la capacité globale d’un biomarqueur quantitatif à guider le choix du traitement. Après une revue de la littérature, une nouvelle méthode basée sur une extension des courbes ROC est proposée, et comparée aux méthodes existantes. Son principal avantage est d’être non paramétrique, et d’être indépendante de l’efficacité moyenne des traitements. Dans un second temps, lorsqu’un biomarqueur prédictif quantitatif est étudié, la définition d’un seuil de marqueur au-delà duquel la première option de traitement sera préférée, et en-deçà duquel la deuxième option de traitement sera préférée se pose. Une approche reposant sur la définition d’une fonction d’utilité est proposée permettant alors de tenir compte de l’efficacité des traitements ainsi que de leur impact sur la qualité de vie des patients. Une méthode Bayésienne d’estimation de ce seuil optimal est proposée / In France, the cancer research is a major public health issue. The number of new cancer cases nearly doubled between 1980 and 2012. The heterogeneity of the tumor characteristics, for a given cancer, presents a great challenge in the research of new effective treatments. In this context, much hope is placed in the research of predictive (or treatment selection) biomarkers that reflect the patients’ characteristics in order to guide treatment choice. For example, in the metastatic colorectal cancer setting, it is admitted that the addition of cetuximab (an anti-EGFR) to classical chemotherapy (the FOLFOX4), only improve the outcome of patients with KRAS wild-type tumors. In that context, the KRAS gene is a binary treatment selection marker, but plenty of biomarkers result from some quantifications or dosage measurements. The first aim of this thesis is to quantify the global treatment selection ability of a biomarker. After a review of the existing litterature, a method based on an extension of ROC curves is proposed and compared to existing methods. Its main advantage is that it is non-parametric, and that it does not depend on the mean risk of event in each treatment arm. In a second time, when a quantitative treatment selection biomarker is assessed, there is a need to estimate a marker thereshold value above which one treatment is preferred, and below which the other treatment is recommended. An approach that relies on the definition of a utility function is proposed in order to take into account both efficacy and toxicity of treatments when estimating the optimal threshold. A Bayesian method for the estimation of the optimal threshold is proposed

Actuellement, bien que la plupart des pays nucléaires converge vers la même solution technique: le stockage profond pour la gestion des déchets radioactifs de haute activité et à vie longue, les objectifs calendaires divergent d'un pays à l'autre. Grâce au calcul économique, nous souhaitons apporter des éléments de réponse à la question suivante : En termes de temporalité, comment les générations présentes, qui bénéficient de la production d'électricité nucléaire, doivent-elles supporter les charges de la gestion des déchets radioactifs en tenant compte des générations futures ? Cette thèse se propose d'analyser spécifiquement la décision française en tenant compte de son contexte. Nous proposons un ensemble d'outils qui permet d'évaluer l'Utilité du projet de stockage profond en fonction des choix de temporalité. Notre thèse étudie également l'influence en retour des choix de stockage sur le cycle du combustible nucléaire. Au-delà, nous prenons en compte les interactions entre le stockage profond et les choix de parc nucléaire et de cycle du combustible qui constituent un « système complet ». / Nowadays, the deep geological repository is generally considered as the reference solution for the definitive management of spent nuclear fuel/high-level waste, but different countries have decided different disposal deployment schedules. Via the economic calculation, we hope to offer some answers to the following question: In terms of disposal time management, how should the present generations, benefiting from the nuclear power generation, bear the costs of radioactive waste management, while taking into account future generations? This thesis proposes to analyze specifically the French decision in its context. We propose a set of tools to evaluate the Utility of the deep geological repository project according to the deployment schedule choices. Our thesis also studies the influence of disposal choices on the nuclear fuel cycle. Beyond, we also take into account the interactions between the deep geological repository, nuclear fleet and cycle choices which constitute a "complete system".

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

附最低保證投資型保險商品的特色在於無論投資者的投資績效好壞，保險金額皆享有一最低投資保證，過去關於此類商品的研究皆假設標的資產為單一資產，或依固定比例之投資組合，並沒有考慮到投資人自行配置投資組合的效果，但大部分市售商品中，投資人可以自行配置投資標，此情況之下，保險公司如何衡量適當的保證成本即為一相當重要之課題。 本研究假設投資人風險偏好服從冪次效用函數，並假設與保單所連結之投資標的有兩種資產，一為具有高風險高報酬的資產，另一為具有低風險低報酬之資產，在每個保單年度之初，投資人可以選擇配置在兩種資產之比例，我們運用黃迪揚(2009)所提出的動態規劃數值解之方法，計算出在考慮投資人自行配置資產之下，保證成本將會比固定比例之投資高出12個百分點。 此外，為了瞭解在不同資產報酬率的模型之下，保證成本是否會有不一樣的結論，除了對數常態模型之外，我們假設高風險資產與低風險資產服從ARIMA-GARCH(Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedastic )模型，並得到較高的保證成本。 / The main characteristic of variable annuities (VA) with minimum benefits is that the benefit will be guaranteed. Previous literatures assume a specific underling asset return process when considering the guaranteed cost of VA; but they do not consider the portfolio choice opportunity of the policyholders. However, it is common for policyholders to rebalance his portfolio in many types of VA products. Therefore it’s important for insurance companies to apply an approximate method to measure the guaranteed cost. In this research, we assume that there are two potential assets in policyholders’ portfolio; one with high risk and high return and the other one with low risk and low return. The utility function of the policyholder is assumed to follow a power utility. We consider the asset allocation effect on the guaranteed cost for a VA with guaranteed minimum withdrawal benefits, finding that the guaranteed cost will increase 12% compared with a specific underling asset. The model effect of the asset return process is also examined by considering two different asset processes, the lognormal model and ARIMA-GARCH model. The solution of dynamic programming problem is solved by the numerical approach proposed by Huang (2009). Finally we get the conclusion which the guaranteed cost given by the ARIMA-GARCH model is greater than the lognormal model.

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.