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Le présent mémoire analyse l'impact du contexte d'insolvabilité sur le devoir fiduciaire d'agir dans le meilleur intérêt de la compagnie, devoir imposer aux administrateurs de compagnies par la législation corporative canadienne. L'objectif du mémoire est de déterminer un standard de conduite à être adopté par l'administrateur d'une compagnie insolvable en vue de répondre à ce devoir fiduciaire. Dans un premier temps, comment peut-on définir ce que constitue le « meilleur intérêt de la compagnie» ? L'auteur en vient à la conclusion que l'intérêt de la compagnie est au carrefour d'une communauté d'intérêts lui étant sous-jacents. L'intérêt de la compagnie, bien qu'indépendant de ces intérêts sous-jacents, ne peut s'analyser en faisant abstraction de ces derniers. La jurisprudence et la doctrine récentes laissent entrevoir que l'impact du contexte d'insolvabilité se fait sentir sur la détermination de ces intérêts sous-jacents à celui de la compagnie susceptibles d'être affectés par la finalité poursuivie par la compagnie, finalité axée sur la maximisation des profits à partir des opérations de l'entreprise exploitée par la compagnie. Dans un contexte d'insolvabilité, le créancier, à l'instar de l'actionnaire dans un contexte de solvabilité, supporte le risque commercial résiduel et doit recevoir une attention appropriée par les administrateurs. Par conséquent, dans la détermination de ce que constitue le meilleur intérêt de la compagnie, l'administrateur ne peut, lorsque la compagnie est insolvable, faire abstraction de l'intérêt des créanciers. Ainsi, dans un deuxième temps, qui sont les véritables bénéficiaires du devoir fiduciaire d'agir dans le meilleur intérêt de la compagnie dans un contexte d'insolvabilité? L'auteur en vient à la conclusion que le créancier est un bénéficiaire indirect de ce devoir fiduciaire lorsque la compagnie est insolvable. Tout comme l'actionnaire dans un contexte de solvabilité, le créancier doit être en mesure d'intenter un recours de nature dérivée en vue d'obtenir réparation, pour et au nom de la compagnie. Le contexte d'insolvabilité fait naître, à l'endroit des administrateurs, une obligation de nature fiduciaire de prendre en considération l'intérêt des créanciers tout en permettant à ces derniers d'intenter un tel recours dérivé en vue d'obtenir réparation à la suite d'une violation du devoir fiduciaire d'agir dans le meilleur intérêt de la compagnie. En plus d'être soutenue par une revue de la législation, de la jurisprudence et de la doctrine canadiennes, cette conclusion s'appuie sur une revue de la législation, de la jurisprudence et de la doctrine de certains pays du Commonwealth (Angleterre, Australie et Nouvelle-Zélande) et des États-Unis, juridictions avec lesquelles le Canada entretient des relations privilégiés, historiquement ou économiquement. Finalement, que doit faire l'administrateur d'une compagnie insolvable en vue de répondre à ce devoir fiduciaire d'agir dans le meilleur intérêt de la compagnie? L'auteur arrive à la conclusion que cette obligation de prendre en considération l'intérêt du créancier dans un contexte d'insolvabilité se traduit par un exercice de conciliation entre les intérêts du créancier et ceux des actionnaires. Les paramètres de cet exercice de conciliation sont déterminés en fonction du scénario envisagé par les administrateurs face à la situation d'insolvabilité. Plus le scénario se rapproche d'une liquidation plus ou moins formelle des actifs tangibles et facilement dissociables de la compagnie, moins cet exercice en sera un de conciliation et plus l'intérêt du créancier devra recevoir une attention prépondérante. À l'opposé, plus le scénario en est un de restructuration fondée sur une relance de l'entreprise exploitée par la compagnie insolvable, plus l'intérêt de l'actionnaire devra recevoir une attention particulière. / The following thesis analyses the impact of a company's insolvency on the fiduciary duties of its directors and officers, as imposed by Canadian corporate law. More specifically it shall examine the repercussions of an insolvency on management's fiduciary duty to act in accordance with the company's best interests. The objective shall therefore be to assess the extent of such fiduciary duty in the context of an insolvency and to establish a guideline to be followed by directors and officers in view of complying with said duty. Firstly, what constitutes the "best interests of the company"? The author concludes that a company's interests are comprised of a community of underlying interests. Although the interests of the company remain independent, it cannot be determined without taking into account said underlying interests. Amongst this community of underlying interests, shareholders and creditors, members of such community that supports the financing of the company's operations, occupy a predominant place. Recent case law and doctrinal authorities have concluded that the impact of a company's insolvency does not affect the ultimate objective pursued by the company, i.e. the maximisation of profit, but rather affects the determination of the members of the community of underlying interests that shall be affected by the pursuit of such finality. As such, in a context of insolvency, creditors, similar to shareholders in a context of solvency, are the residual risk-bearers of the company's commercial expenditure. Consequently, in view of determining what constitutes the best interests of the company, when it is insolvent, directors and officers may not ignore the creditors' interests. Secondly, who are the real beneficiaries of the fiduciary duty to act in a company's best interests when it becomes insolvent? The author concludes that creditors are indirect beneficiaries of such fiduciary duty in a context of insolvency. Similarly to shareholders in a context of solvency, creditors must be entitled to institute a derivative claim against directors and officers in order to obtain, in the name and for the company, compensation for the violation of said fiduciary duty. Insolvency triggers the existence of an obligation, fiduciary in nature, to take into account the creditors' interests. As such, directors and officers are to consider the creditors' interests in exercising their fiduciary duty to act in strict compliance with the best interests of the company. This conclusion is based on a review of the Canadian statutory law, jurisprudence and doctrinal authorities. Furthermore, this conclusion is supported by a review of same from certain Commonwealth jurisdictions (England, Australia and New-Zealand) and from the United States of America, jurisdictions with whom Canada has a privileged relationship, historically and/or economically. Finally, how does the obligation to take into account the creditors' interests translate in practice for directors and officers of an insolvent company? The author concludes that the obligation to take into account the creditors' interests is, in reality, an obligation to reconcile the shareholders' and creditors' interests with that of the company's best interests. The parameters of such obligation shall be determined with respect to the scenario conceived by directors and officers in order to effectively manage a situation of insolvency. Should such scenario focus on the liquidation of the core assets of the company, then the interests of the shareholders shall be subjugated to that of the creditors'. Conversely, should such scenario focus on the reorganisation of the company's commercial expenditures, based on the company's existing structures, then the shareholder's interest shall receive a more extensive attention by directors and officers.

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

Generalized linear mixture models (GLMM) are widely used in statistical applications to model count and binary data. We consider the problem of nonparametric likelihood estimation of mixing distributions in GLMM's with multiple random effects. The log-likelihood to be maximized has the general form l(G)=Σi log∫f(yi,γ) dG(γ) where f(.,γ) is a parametric family of component densities, yi is the ith observed response dependent variable, and G is a mixing distribution function of the random effects vector γ defined on Ω. The literature presents many algorithms for maximum likelihood estimation (MLE) of G in the univariate random effect case such as the EM algorithm (Laird, 1978), the intra-simplex direction method, ISDM (Lesperance and Kalbfleish, 1992), and vertex exchange method, VEM (Bohning, 1985). In this dissertation, the constrained Newton method (CNM) in Wang (2007), which fits GLMM's with random intercepts only, is extended to fit clustered datasets with multiple random effects. Owing to the general equivalence theorem from the geometry of mixture likelihoods (see Lindsay, 1995), many NPMLE algorithms including CNM and ISDM maximize the directional derivative of the log-likelihood to add potential support points to the mixing distribution G. Our method, Direct Search Directional Derivative (DSDD), uses a directional search method to find local maxima of the multi-dimensional directional derivative function. The DSDD's performance is investigated in GLMM where f is a Bernoulli or Poisson distribution function. The algorithm is also extended to cover GLMM's with zero-inflated data. Goodness-of-fit (GOF) and selection methods for mixed models have been developed in the literature, however their application in models with nonparametric random effects distributions is vague and ad-hoc. Some popular measures such as the Deviance Information Criteria (DIC), conditional Akaike Information Criteria (cAIC) and R2 statistics are potentially useful in this context. Additionally, some cross-validation goodness-of-fit methods popular in Bayesian applications, such as the conditional predictive ordinate (CPO) and numerical posterior predictive checks, can be applied with some minor modifications to suit the non-Bayesian approach. / Graduate / 0463 / rabihsaab@gmail.com

Recent developments show that derivative free methods are highly demanded by researches for solving optimization problems in various practical contexts. Although well-known optimization methods that employ derivative information can be very effcient, a derivative free method will be more effcient in cases where the objective function is nondifferentiable, the derivative information is not available or is not reliable. Derivative Free Optimization (DFO) is developed for solving small dimensional problems (less than 100 variables) in which the computation of an objective function is relatively expensive and the derivatives of the objective function are not available. Problems of this nature more and more arise in modern physical, chemical and econometric measurements and in engineering applications, where computer simulation is employed for the evaluation of the objective functions. In this thesis, we give an example of the implementation of DFO in an approach for optimizing stirrer configurations, including a parametrized grid generator, a flow solver, and DFO. A derivative free method, i.e., DFO is preferred because the gradient of the objective function with respect to the stirrer&rsquo / s design variables is not directly available. This nonlinear objective function is obtained from the flow field by the flow solver. We present and interpret numerical results of this implementation. Moreover, a contribution is given to a survey and a distinction of DFO research directions, to an analysis and discussion of these. We also state a derivative free algorithm used within a clustering algorithm in combination with non-smooth optimization techniques to reveal the effectiveness of derivative free methods in computations. This algorithm is applied on some data sets from various sources of public life and medicine. We compare various methods, their practical backgrounds, and conclude with a summary and outlook. This work may serve as a preparation of possible future research.

Video editing and object recognition are two significant fields in computer vi- sion: the first has remarkably assisted digital production and post-production tasks of a digital video footage; the second is considered fundamental to image classification or image based search in large databases (e.g. the web). In this thesis, we address two problems, namely we present a novel formulation that tackles video editing tasks and we develop a mechanism that allows to generate more robust descriptors for objects in an image. Concerning the first problem, this thesis proposes two variational models to perform temporally coherent video editing. These models are applied to change an object’s (rigid or non-rigid) texture throughout a given video sequence. One model is based on propagating color information from a given frame (or be- tween two given frames) along the motion trajectories of the video; while the other is based on propagating gradient domain information. The models we present in this thesis require minimal user intervention and they automatically accommodate for illumination changes in the scene. Concerning the second problem, this thesis addresses the problem of affine invariance in object recognition. We introduce a way to generate geometric affine invariant quantities that are used in the construction of feature descrip- tors. We show that when these quantities are used they do indeed achieve a more robust recognition than the state of the art descriptors. i / La edición de vídeo y el reconocimiento de objetos son dos áreas fundamentales en el campo de la visión por computador: la primera es de gran utilidad en los procesos de producción y post-producción digital de vídeo; la segunda es esencial para la clasificación o búsqueda de imágenes en grandes bases de datos (por ejemplo, en la web). En esta tesis se acometen ambos problemas, en concreto, se presenta una nueva formulación que aborda las tareas de edición de vídeo y se desarrolla un mecanismo que permite generar descriptores más robustos para los objetos de la imagen. Con respecto al primer problema, en esta tesis se proponen dos modelos variacionales para llevar a cabo la edición de vídeo de forma coherente en el tiempo. Estos modelos se aplican para cambiar la textura de un objeto (rígido o no) a lo largo de una secuencia de vídeo dada. Uno de los modelos está basado en la propagación de la información de color desde un determinado cuadro de la secuencia de vídeo (o entre dos cuadros dados) a lo largo de las trayectorias de movimiento del vídeo. El otro modelo está basado en la propagación de la información en el dominio del gradiente. Ambos modelos requieren una intervención mínima por parte del usuario y se ajustan de manera automática a los cambios de iluminación de la escena. Con respecto al segundo problema, esta tesis aborda el problema de la invariancia afín en el reconocimiento de objetos. Se introduce un nuevo método para generar cantidades geométricas afines que se utilizan en la generación de descriptores de características. También se demuestra que el uso de dichas cantidades proporciona mayor robustez al reconocimiento que los descriptores existentes actualmente en el estado del arte.

How should Australian criminal trial courts treat evidence deriving from illegally or improperly obtained evidence? The fact that derivative evidence gives rise to factors distinct from primary evidence makes it deserving of an examination of its peculiarities. In doing so, the assumption may be put aside that derivative evidence falls wholly within the established general discourse of illegally or improperly obtained evidence. Just as the judicial response to primary evidence must be intellectually rigorous, disciplined and principled, so must be the response to derivative evidence. As such, a principled analysis of how Australian courts should approach derivative evidence can significantly contribute to the discourse on the law with respect to the exclusion of illegally or improperly obtained evidence. This thesis provides that principled analysis by arguing that the principles which underpin and inform the discretionary exclusionary frameworks within Australia require an approach which is consistent as between illegally obtained derivative evidence and illegally obtained primary evidence.

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.

Thesis (PhD)--Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics, 2008. / Bibliography: p. 73-77. / Introduction -- Lévy processes used in option pricing -- Option pricing for Lévy processes -- Option pricing based on empirical characteristic functions -- Performance of the five models on historical data -- Conclusions -- References -- Appendix A. Proofs -- Appendix B. Supplements -- Appendix C. Matlab programs. / Pricing problems of financial derivatives are among the most important ones in Quantitative Finance. Since 1973 when a Nobel prize winning model was introduced by Black, Merton and Scholes the Brownian Motion (BM) process gained huge attention of professionals professionals. It is now known, however, that stock market log-returns do not follow the very popular BM process. Derivative pricing models which are based on more general Lévy processes tend to perform better. --Carr & Madan (1999) and Lewis (2001) (CML) developed a method for vanilla options valuation based on a characteristic function of asset log-returns assuming that they follow a Lévy process. Assuming that at least part of the problem is in adequate modeling of the distribution of log-returns of the underlying price process, we use instead a nonparametric approach in the CML formula and replaced the unknown characteristic function with its empirical version, the Empirical Characteristic Functions (ECF). We consider four modifications of this model based on the ECF. The first modification requires only historical log-returns of the underlying price process. The other three modifications of the model need, in addition, a calibration based on historical option prices. We compare their performance based on the historical data of the DAX index and on ODAX options written on the index between the 1st of June 2006 and the 17th of May 2007. The resulting pricing errors show that one of our models performs, at least in the cases considered in the project, better than the Carr & Madan (1999) model based on calibration of a parametric Lévy model, called a VG model. --Our study seems to confirm a necessity of using implied parameters, apart from an adequate modeling of the probability distribution of the asset log-returns. It indicates that to precisely reproduce behaviour of the real option prices yet other factors like stochastic volatility need to be included in the option pricing model. Fortunately the discrepancies between our model and real option prices are reduced by introducing the implied parameters which seem to be easily modeled and forecasted using a mixture of regression and time series models. Such approach is computationaly less expensive than the explicit modeling of the stochastic volatility like in the Heston (1993) model and its modifications. / Mode of access: World Wide Web. / x, 111 p. ill., charts