In this work we study two problems motivated by Risk Management: the optimal design of financial products from an investor's point of view and the calculation of bounds and approximations for sums involving non-independent random variables. The element that interconnects these two topics is the notion of conditioning, a fundamental concept in probability and statistics which appears to be a useful device in finance. In the first part of the dissertation, we analyse structured products that are now widespread in the banking and insurance industry. These products typically protect the investor against bearish stock markets while offering upside participation when the markets are bullish. Examples of these products include capital guaranteed funds commercialised by banks, and equity linked contracts sold by insurers. The design of these products is complex in general and it is vital to examine to which extent they are actually interesting from the investor's point of view and whether they cannot be dominated by other strategies. In the academic literature on structured products the focus has been almost exclusively on the pricing and hedging of these instruments and less on their performance from an investor's point of view. In this work we analyse the attractiveness of these products. We assess the theoretical cost of inefficiency when buying a structured product and describe the optimal strategy explicitly if possible. Moreover we examine the cost of the inefficiency in practice. We extend the results of Dybvig (1988a, 1988b) and Cox & Leland (1982, 2000) who in the context of a complete, one-dimensional market investigated the inefficiency of path-dependent pay-offs. In the dissertation we consider this problem in one-dimensional Levy and multidimensional Black-Scholes financial markets and we provide evidence that path-dependent pay-offs should not be preferred by decision makers with a fixed investment horizon, and they should buy path-independent structures instead. In these market settings we also demonstrate the optimal contract that provides the given distribution to the consumer, and in the case of risk- averse investors we are able to propose two ways of improving the design of financial products. Finally we illustrate the theory with a few well-known securities and strategies e.g. dollar cost averaging, buy-and-hold investments and widely used portfolio insurance strategies. The second part of the dissertation considers the problem of finding the distribution of a sum of non- independent random variables. Such dependent sums appear quite often in insurance and finance, for instance in case of the aggregate claim distribution or loss distribution of an investment portfolio. An interesting avenue to cope with this problem consists in using so-called convex bounds, studied by Dhaene et al. (2002a, 2002b), who applied these to sums of log-normal random variables. In their papers they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In the dissertation we prove that unlike the log-normal case the construction of a convex lower bound in explicit form appears to be out of reach for general sums of log-elliptical risks and we show how we can construct stop-loss bounds and we use these to construct mean preserving approximations for general sums of log-elliptical distributions in explicit form. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Les juges sont devenus des acteurs omniprésents au sein des sociétés. Garants de l’application du droit, leurs nombreuses interventions contribuent au bon fonctionnement des sociétés. L’étude des interventions judiciaires spécifiques au droit des sociétés in bonis permet de souligner le rôle majeur désormais tenu par les juges. L’analyse des pouvoirs judiciaires de régulation de la vie sociétaire et de sanction des obligations civiles en droit des sociétés met en évidence l’impact des interventions judiciaires sur le fonctionnement des sociétés. Il existe de nombreuses procédures spécifiques au droit des sociétés, mais la richesse des solutions et des innovations jurisprudentielles caractérise également le recours nécessaire au droit civil et au droit processuel afin de répondre aux exigences de l’environnement sociétaire. Fort de ce constat, différentes pistes peuvent être proposées dans le but de renforcer l’efficacité et l’utilité de ces interventions judiciaires qui permettent de garantir l’efficience et l’attractivité du droit des sociétés français. / Judges have become ubiquitous stakeholders within companies. As guardians of law, they play a real role in the well being of companies. The study of legal interventions, specific to corporate law, applied to “in bonis” companies clearly highlights the major role played by judges today. Analysis of the judiciary powers regulating companies lives and of the sanctions surrounding liabilities in corporate law puts emphasis on the impact of judicial involvement on company functioning. Many specific corporate law proceedings exist, however, the rich range in solutions and case-law innovations accentuates the need to resort to civil and procedural law in response to the business world’s requirements and expectations. With this in mind, different lines of action are imaginable in the hope to reinforce the usefulness and relevance of judicial involvement that guarantee the efficiency and attractive nature of French corporate law.

The diploma thesis is divided into four main parts. The first part deals with the issue of waste management and its energy utilization in waste incineration. Processed harmful substances produced by incineration as well as emission limits. It deals with the types of catalytic carriers, their description, production and more detailed processing of ceramic foam VUKOPOR. The second part is devoted to technologies utilizing catalytic processes and a more detailed specification of the process. In the third part there is processed the calculation methods for pressure losses for individual types of carriers. Fourth, the most extensive part describes the INTEQII experimental device, its technology and construction, as well as the principle of the practical part, measuring of the pressure losses of carriers. It includes the evaluation of pressure losses in separate categories of carriers, such as the bed, HoneyComb and VUKOPOR ceramic foam. Subsequently, a comparison of the pressure losses of all carriers is made relative to the reference size of 1 m. The impact of bonding of VUKOPOR foam samples on the size of pressure losses is discussed. At the end of this section, the suitability of calculation methods for individual carriers is evaluated, depending on the experimental pressure loss data.