In all their various categories, the arts serve as the dominant subject matter of Gesamtkunstwerk and Other Trifles. The title itself begins with a German word-meld—gesamt (total) + kunstwerk (work of art). Thus a primary aim of these poems is to bring as many elements of art together as possible and to use their various forms (self-portraits, nocturnes, odes, etc.) as metaphorical frameworks that inform abstractions such as regret ("How to Draw Regret"), psychological disorders ("Insomnia Nocturnes") and confusion in how one should feel about living realities as opposed to inanimate objects ("Dead Starling"). Most of the poems that are not related in some way to the arts (other than their inseparable relation to the art of poetry itself) deal with death or some other form of loss. Some of them humorous ("Commencement Speech"), others poignant ("In Places Where We Store Our Deaths"), these poems ironically find their place as the "other trifles" of the work. The purpose of this somewhat irreverent categorization of death and tragedy is to create ironic commentaries on the triviality of humankind's grand designs and accomplishments and to show the many similarities shared by comedy and tragedy alike, a project Tony Hoagland took up in his first book of poems, Sweet Ruin. My aim in writing these poems is to better understand how various art forms relate to each other and how aligning those arts in poetry allows the various genres to be "in conversation" one with another. I hope that readers will come away with a better understanding of how art forms are interconnected, but at the same time, I always aim to construct my poems in such a way that multiple readings can occur.

To re-purpose an abandoned wine cooperative into a set of workshops and studios with a focus on re-interpreting the role of the ‘crafts apprentice’ in a contemporary setting. The project hopes to upsurge society’s interest in the cultural value that such skills and products hold today, as a way of ceasing the decrasing number of dissapearing crafts and craftmen and women. Simultaneously and above all, the main effect that the interventions to this building and the activities taking place is hoping to have, is to add a transcendental societal, communal and sociological value for our community.

Pour respecter les droits d’auteur, la version électronique de ce mémoire a été dépouillée de certains documents visuels. La version intégrale du mémoire a été déposée au Service de la gestion des documents et des archives de l'Université de Montréal / Que peuvent être des images pour la paix? Nous supposons que les agencements fictionnels des matières de l’expression capables d’entrouvrir la perception habituelle des choses et d’impulser de nouvelles visions du monde, en direction d’un vivre ensemble plus pacifique, sont ceux qui reposent sur trois modalités de respect. Premièrement, respect de l’intelligence des subjectivités spectatorielles, de leur capacité à lire et traduire par elles-mêmes ce qui leur est présenté. Deuxièmement, respect des êtres dans leur multiplicité, du caractère fondamentalement entre-formes de l’existence. Enfin, respect des potentialités expressives portées par les corps anonymes, humains autant que matériels, des virtualités créatrices que recèlent leurs impressions muettes. Nous retrouvons ces trois postures, à la fois esthétiques et politiques, dans le cinéma de Jia Zhang-ke. En effet, le travail fictionnel de ce véritable conteur consiste à débusquer la richesse sensible de l’expérience commune et à en opérer une réimagination fertile, notamment par le métissage fabulatoire de diverses paroles historiques ou encore par la revitalisation de décors ruiniformes au sein de natures mortes animées. Les gestes malicieux de cet artiste inquiètent et multiplient la figure donnée au réel et, par le fait même, suscitent de nouvelles manières de percevoir, de (re)connaître, de penser, voire de se constituer. À travers ses images, le commun s’exprime, se crée une mémoire et obtient la possibilité de devenir autre. / What can be images for peace? We suppose that the fictional arrangements of the expressive materials able to expand the usual perception of things and provoke new visions of the world, in direction of a better living together, are the ones which are based on three modalities of respect. Firstly, respect of the spectatorial subjectivities’ intelligence, of their capacity to read and translate by themselves what they are seeing. Secondly, respect of the beings in their multiplicity, of the fundamental in-between-forms attribute of the existence. Finally, respect of the expressive potentials carry by the anonymous bodies, human as well as material, of the virtualities of creation contain in their mute impressions. We find those three aesthetical and political postures in the cinema of Jia Zhang-ke. In effect, the fictional work of this true teller consists in finding the “sensible richness” of the common experience and in operating a fertile reimagination of this one, for instance by interbreeding, with a fabulating manner, various historic speeches or by revitalizing sceneries of ruins in animated still lifes. The mischievous gestures of this artist trouble and multiply the figure given to the real and, consequently, develop new ways of perceiving, knowing, thinking, and even of emerging. Through his images, the common express himself, creates himself a memory and has the opportunity to become something else.

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent. / This master thesis is concerned with risk theory, and more specifically with actuarial surplus models with dividends. We focus on an important model, called the gamma-omega model, which is built to enable the study of both periodic dividend distributions and a non-standard type of ruin. We make several new extensions to this model, which are motivated by solvency considerations. The first one consists in adapting results from a 2011 paper to a new model built on the assumption of a solvency constraint. The second one, more elaborate, consists in proving the optimality of a barrier strategy to pay dividends in the gamma-omega model. The third one deals with the adaptation of a 2003 theorem on the optimality of barrier strategies in the case of solvency constraints, which was not proved right in the periodic dividend framework. We also give analogous results to the 2011 paper in case of an optimal barrier under the solvency constraint. Finally, the last one is concerned with two non-traditional ways of dealing with a ruin event. We first implement a forced liquidation of the surplus in parallel with a possibility of liquidation at first opportunity in case of bad prospects for the dividends. Secondly, we deal with injections of capital into the company reserve, and monitor their implications on the amount of expected dividends. Numerical illustrations are provided in each section, when relevant.

Title: Large deviations and their applications in insurance mathematics Author: Lucia Fuchsová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Supervisor's e-mail address: Zbynek.Pawlas@mff.cuni.cz Abstract: In the present work we study large deviations theory. We discuss heavy-tailed distributions, which describe the probability of large claim oc- curence. We are interested in the use of large deviations theory in insurance. We simulate claim sizes and their arrival times for Cramér-Lundberg model and first we analyze the probability that ruin happens in dependence on the parameters of our model for Pareto distributed claim size, next we compare ruin probability for other claim size distributions. For real life data we model the probability of large claim size occurence by generalized Pareto distribu- tion. 1

Le travail présenté ici a pour but d’évaluer l’influence de surcharges incidentelles sur le comportement en fatigue de tôles en acier soudées par points et destinées à une application automobile. Une campagne d’essais expérimentale sur éprouvettes a permis d’établir les courbes effort – durée de vie de trois nuances d’acier soudées par point et soumis à des sollicitations de traction-cisaillement soit à amplitude constante (courbe de référence), soit avec des sollicitations incidentelles survenant à raison d’un cycle de surcharge pour 100 cycles appliqués. Les éprouvettes utilisées sont constituées de deux rectangles de tôle assemblés par un point soudé réalisé par un soudage par résistance. Deux rapports de surcharge, 1,4 et 2,3, sont testés et analysés. L’ensemble des cycles de tous les chargements présente le rapport de charge de 0,1 (traction ondulée). Pour deux nuances d’acier, les surcharges périodiques sont bénéfiques à la tenue en fatigue, ils permettent d’augmenter sensiblement la durée de vie. Pour la troisième nuance d’acier en revanche, l’effet enregistré est un affaissement très marqué des propriétés de fatigue. Deux types de ruine par fatigue sont observés, l’un par fissuration des tôles au droit du congé de raccordement du noyau fondu du point soudé sur la tôle, du côté de la zone en traction. L’autre se traduit par un cisaillement du noyau fondu dans le plan de sa section droite minimale et ne se produit qu’à haut niveau d’effort appliqué. Ces calculs par Eléments finis ont mis en évidence des états de contraintes multiaxiaux, principalement de traction et de cisaillement dans les zones expérimentales d’amorçage et de fissuration des éprouvettes. Il est observé de façon très claire une prépondérance de la contrainte de traction là où s’amorce la fissure de fatigue conduisant à la ruine de l’éprouvette par fissuration complète d’une des deux tôles, et une prépondérance tout aussi évidente de la contrainte de cisaillement dans la section minimale du noyau fondu du point soudé où se produit dans certains cas la rupture du point soudé par cisaillement. Les calculs effectués corroborent donc très bien les observations expérimentales. L’utilisation de nouvelles lois d’endommagement basées sur un cumul non linéaire du dommage, dont une qui a été proposée au laboratoire, conduit à une prévision des durées de vie en bon accord avec l’expérimentation alors que la loi de Miner demeure pour sa part très éloignée des résultats expérimentaux. / The objective of this work is to evaluate the influence of incidental overloads on the fatigue behavior of steel plates welded by points and aimed for automobile application. An experimental test campaign on specimens had allowed the establishment of effort curves – life cycle of three types of steel welded by points and subjected to tensile-shear efforts under constant amplitude (reference curve), and with incidental overloads happening once (overloaded cycle) for 100 applied cycles. Specimens used in the test are made of two rectangle plates joined by a welded point and done by resistance welding. Two overloads ratio, 1,4 and 2,3 were tested and analyzed. The overall overloading cycle presents the ratio of 0,1 (undulated tensile effort). For two out of three steel types, the periodicals overloading are benefit in term of fatigue resisting, their life duration has been slightly improved. The third steel type has in contrary showed observable deterioration of fatigue properties.Two types of ruin by fatigue have been observed. The first one shows cracking of plates on the right axle journal fillet of the melted nucleus of the welded point on the plate, in the tensile zone side. The second is showed by a shearing of the melted nucleus in the plan of its minimal right “section” and this happens at a high level of applied effort. Calculation done using Finite Elements method has evidently showed states of multiaxial stresses essentially tensile stress and shearing stress in the experimental areas of starting and cracking of specimens. It is clearly observed a mainly dominant tensile stress where the fatigue cracking starts leading to the ruin of the specimen by the complete cracking of one of the two plates, and also evidently a mainly dominant shearing stress in the minimal section of the melted nucleus of welded point, where in some case the rupture by shearing of the welded point is observed. The calculations done are then in total agreement with the experimental observations. The use of new damage laws, which one has been proposed in the laboratory based on a nonlinear cumulating of damage, leads to a forecasting of life duration in accordance with experimentation while the Miner law results stays far away from the experimental results.

Initialement, la théorie du risque supposait l’indépendance entre les différentes variables aléatoires et autres paramètres intervenant dans la modélisation actuarielle. De nos jours, cette hypothèse d’indépendance est souvent relâchée afin de tenir compte de possibles interactions entre les différents éléments des modèles. Dans cette thèse, nous proposons d’introduire des modèles de dépendance pour différents aspects de la théorie du risque. Dans un premier temps, nous suggérons l’emploi des copules comme structure de dépendance. Nous abordons tout d’abord un problème d’allocation de capital basée sur la Tail-Value-at-Risk pour lequel nous supposons un lien introduit par une copule entre les différents risques. Nous obtenons des formules explicites pour le capital à allouer à l’ensemble du portefeuille ainsi que la contribution de chacun des risques lorsque nous utilisons la copule Farlie-Gumbel-Morgenstern. Pour les autres copules, nous fournissons une méthode d’approximation. Au deuxième chapitre, nous considérons le processus aléatoire de la somme des valeurs présentes des sinistres pour lequel les variables aléatoires du montant d’un sinistre et de temps écoulé depuis le sinistre précédent sont liées par une copule Farlie-Gumbel-Morgenstern. Nous montrons comment obtenir des formes explicites pour les deux premiers moments puis le moment d’ordre m de ce processus. Le troisième chapitre suppose un autre type de dépendance causée par un environnement extérieur. Dans le contexte de l’étude de la probabilité de ruine d’une compagnie de réassurance, nous utilisons un environnement markovien pour modéliser les cycles de souscription. Nous supposons en premier lieu des temps de changement de phases de cycle déterministes puis nous les considérons ensuite influencés en retour par les montants des sinistres. Nous obtenons, à l’aide de la méthode d’erlangisation, une approximation de la probabilité de ruine en temps fini. / Initially, it was supposed in risk theory that the random variables and other parameters of actuarial models were independent. Nowadays, this hypothesis is often relaxed to take into account possible interactions. In this thesis, we propose to introduce some dependence models for different aspects of risk theory. In a first part, we use copulas as dependence structure. We first tackle a problem of capital allocation based on the Tail-Value-at-Risk where the risks are supposed to be dependent according to a copula. We obtain explicit formulas for the capital to be allocated to the overall portfolio but also for the contribution of each risk when we use a Farlie-Gumbel-Morenstern copula. For the other copulas, we give an approximation method. In the second chapter, we consider the stochastic process of the discounted aggregate claims where the random variables for the claim amount and the time since the last claim are linked by a Farlie-Gumbel-Morgenstern copula. We show how to obtain exact expressions for the first two moments and for the moment of order m of the process. The third chapter assumes another type of dependence that is caused by an external environment. In the context of the study of the ruin probability for a reinsurance company, we use a Markovian environment to model the underwriting cycles. We suppose first deterministic cycle phase changes and then that these changes can also be influenced by the claim amounts. We use the erlangization method to obtain an approximation for the finite time ruin probability.

The aim of this thesis is to develop algorithmic methods for computing particular performance measures of interest for a general class of discrete-based insurance risk models. We build upon and generalize the insurance risk models considered by Drekic and Mera (2011) and Alfa and Drekic (2007), by incorporating a threshold-based dividend system in which dividends only get paid provided some period of good financial health is sustained above a pre-specified threshold level. We employ two fundamental methods for calculating the performance measures under the more general framework. The first method adopts the matrix-analytic approach originally used by Alfa and Drekic (2007) to calculate various ruin-related probabilities of interest such as the trivariate distribution of the time of ruin, the surplus prior to ruin, and the deficit at ruin. Specifically, we begin by introducing a particular trivariate Markov process and then expressing its transition probability matrix in a block-matrix form. From this characterization, we next identify an initial probability vector for the process, from which certain important conditional probability vectors are defined. For these vectors to be computed efficiently, we derive recursive expressions for each of them. Subsequently, using these probability vectors, we derive expressions which enable the calculation of conditional ruin probabilities and, from which, their unconditional counterparts naturally follow. The second method used involves the first claim conditioning approach (i.e., condition on knowing the time the first claim occurs and its size) employed in many ruin theoretic articles including Drekic and Mera (2011). We derive expressions for the finite-ruin time based Gerber-Shiu function as well as the moments of the total dividends paid by a finite time horizon or before ruin occurs, whichever happens first. It turns out that both functions can be expressed in elegant, albeit long, recursive formulas. With the algorithmic derivations obtained from the two fundamental methods, we next focus on computational aspects of the model class by comparing six different types of models belonging to this class and providing numerical calculations for several parametric examples, highlighting the robustness and versatility of our model class. Finally, we identify several potential areas for future research and possible ways to optimize numerical calculations.

The aim of this thesis is to develop algorithmic methods for computing particular performance measures of interest for a general class of discrete-based insurance risk models. We build upon and generalize the insurance risk models considered by Drekic and Mera (2011) and Alfa and Drekic (2007), by incorporating a threshold-based dividend system in which dividends only get paid provided some period of good financial health is sustained above a pre-specified threshold level. We employ two fundamental methods for calculating the performance measures under the more general framework. The first method adopts the matrix-analytic approach originally used by Alfa and Drekic (2007) to calculate various ruin-related probabilities of interest such as the trivariate distribution of the time of ruin, the surplus prior to ruin, and the deficit at ruin. Specifically, we begin by introducing a particular trivariate Markov process and then expressing its transition probability matrix in a block-matrix form. From this characterization, we next identify an initial probability vector for the process, from which certain important conditional probability vectors are defined. For these vectors to be computed efficiently, we derive recursive expressions for each of them. Subsequently, using these probability vectors, we derive expressions which enable the calculation of conditional ruin probabilities and, from which, their unconditional counterparts naturally follow. The second method used involves the first claim conditioning approach (i.e., condition on knowing the time the first claim occurs and its size) employed in many ruin theoretic articles including Drekic and Mera (2011). We derive expressions for the finite-ruin time based Gerber-Shiu function as well as the moments of the total dividends paid by a finite time horizon or before ruin occurs, whichever happens first. It turns out that both functions can be expressed in elegant, albeit long, recursive formulas. With the algorithmic derivations obtained from the two fundamental methods, we next focus on computational aspects of the model class by comparing six different types of models belonging to this class and providing numerical calculations for several parametric examples, highlighting the robustness and versatility of our model class. Finally, we identify several potential areas for future research and possible ways to optimize numerical calculations.

In this thesis, the discrete time risk model with inhomogeneous claims is considered. This model is used for describing the insurer‘s capital and its components: initial capital, premiums received, and claims paid. The main risk measures, ruin probabilities and Gerber-Shiu function, are investigated and recursive formulas are obtained. These formulas give fast and accurate evaluation of the finite time ruin probabilities and Gerber-Shiu function. However, the infinite time investigations require that the Gerber-Shiu function's values for the initial capital equal to 0 must be known. This is slightly more difficult due to the claim inhomogeneity and for this reason a theorem with explicit expression of the infinite time Gerber-Shiu function for a zero initial capital is proposed. However, for the calculation of the infinite time values, some assumption about underlying claim structure must be made. As a solution the cyclically distributed claims are proposed, the algorithms for application of the theorems are given and numerical examples with graphical output are presented. Finally, a special case of discrete time risk model with inhomogeneous claims distributed according geometric law is investigated. In addition to the main results, another discrete time risk model with inhomogeneous claims acquiring rational values is investigated. Two theorems for evaluation of the finite time ruin probabilities are proved and some examples are presented. / Disertaciniame darbe nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis. Šis modelis aprašo draudimo įmonės turtą įtakojančius veiksnius: pradinį kapitalą, gaunamas įmokas, išmokamas žalas. Išvedamos rekursinės formulės, kurių pagalba galima tiksliai ir greitai rasti baigtinio laiko bankroto tikimybių ir Gerber-Shiu funkcijos vertes. Rekursinės formulės taip pat pateikiamos ir begalinio laiko rizikos matams, tačiau nevienodai pasiskirsčiusių žalų atveju iškyla papildomų sunkumų randant bankroto tikimybę ir Gerber-Shiu funkciją, kai pradinis kapitalas lygus 0. Tam įrodoma atskira teorema, tačiau nedarant jokių prielaidų apie žalų pasiskirstymus, apskaičiuoti vertes lengva tikrai nėra. Kaip išeitis pasiūloma cikliškai pasiskirsčiusių žalų struktūra ir pateikiami algoritmai, leidžiantys teoremas pritaikyti praktiškai. Demonstruojant teoremų ir rekursinių formulių veikimą, pateikiami skaitiniai pavyzdžiai su grafinėmis iliustracijomis bei programų kodai. Galiausiai nagrinėjamas atskiras diskretaus laiko rizikos modelio atvejis, kai žalos pasiskirsčiusios skirtingai pagal geometrinį dėsnį. Disertacijoje taip pat yra nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis, kurios įgyja racionalias reikšmes, bei kintančiomis įmokomis ir pradiniu kapitalu, taip pat įgyjančiais racionalias reikšmes su tam tikra sąlyga. Įrodomos dvi teoremos kaip rasti tokio modelio baigtinio laiko bankroto tikimybę ir keli... [toliau žr. visą tekstą]