Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8.

Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted penalty function not only provides a systematic platform to jointly analyze various quantities of interest, but also offers the convenience to extract key pieces of information from a risk management perspective. For example, by eliminating the penalty function, the Gerber-Shiu function becomes the Laplace-Stieltjes transform of the time to ruin, inversion of which results in a series expansion for the associated density of the time to ruin (see, e.g., Dickson and Willmot (2005)). In this thesis, we propose to analyze the long-standing finite-time ruin problem by incorporating the number of claims until ruin into the Gerber-Shiu analysis. As will be seen in Chapter 2, many nice analytic properties of the original Gerber-Shiu function are preserved by this generalized analytic tool. For instance, the Gerber-Shiu function still satisfies a defective renewal equation and can be generally expressed in terms of some roots of Lundberg's generalized equation in the Sparre Andersen risk model. In this thesis, we propose not only to unify previous methodologies on the study of the density of the time to ruin through the use of Lagrange's expansion theorem, but also to provide insight into the nature of the series expansion by identifying the probabilistic contribution of each term in the expansion through analysis involving the distribution of the number of claims until ruin. In Chapter 3, we study the joint generalized density of the time to ruin and the number of claims until ruin in the classical compound Poisson risk model. We also utilize an alternative approach to obtain the density of the time to ruin based on the Lagrange inversion technique introduced by Dickson and Willmot (2005). In Chapter 4, relying on the Lagrange expansion theorem for analytic inversion, the joint density of the time to ruin, the surplus immediately before ruin and the number of claims until ruin is examined in the Sparre Andersen risk model with exponential claim sizes and arbitrary interclaim times. To our knowledge, existing results on the finite-time ruin problem in the Sparre Andersen risk model typically involve an exponential assumption on either the interclaim times or the claim sizes (see, e.g., Borovkov and Dickson (2008)). Among the few exceptions, we mention Dickson and Li (2010, 2012) who analyzed the density of the time to ruin for Erlang-n interclaim times. In Chapter 5, we propose a significant breakthrough by utilizing the multivariate version of Lagrange's expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely when interclaim times are distributed as a combination of n exponentials. It is worth emphasizing that this technique can also be applied to other areas of applied probability. For instance, the proposed methodology can be used to obtain the distribution of some first passage times for particular stochastic processes. As an illustration, the duration of a busy period in a queueing risk model will be examined. Interestingly, the proposed technique can also be used to analyze some first passage times for the compound Poisson processes with diffusion. In Chapter 6, we propose an extension to Kendall's identity (see, e.g., Kendall (1957)) by further examining the distribution of the number of jumps before the first passage time. We show that the main result is particularly relevant to enhance our understanding of some problems of interest, such as the finite-time ruin probability of a dual compound Poisson risk model with diffusion and pricing barrier options issued on an insurer's stock price. Another closely related quantity of interest is the so-called occupation times of the surplus process below zero (also referred to as the duration of negative surplus, see, e.g., Egidio dos Reis (1993)) or in a certain interval (see, e.g., Kolkovska et al. (2005)). Occupation times have been widely used as a contingent characteristic to develop advanced derivatives in financial mathematics. In risk theory, it can be used as an important risk management tool to examine the overall health of an insurer's business. The main subject matter of Chapter 7 is to extend the analysis of occupation times to a class of renewal risk processes. We provide explicit expressions for the duration of negative surplus and the double-barrier occupation time in terms of their Laplace-Stieltjes transform. In the process, we revisit occupation times in the content of the classical compound Poisson risk model and examine some results proposed by Kolkovska et al. (2005). Finally, some concluding remarks and discussion of future research are made in Chapter 8.

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Made available in DSpace on 2015-03-03T15:28:30Z (GMT). No. of bitstreams: 1 CarlosAGS_DISSERT.pdf: 446797 bytes, checksum: 18c0fd9fe8336f2abf045fa977920e6c (MD5) Previous issue date: 2010-03-19 / In this work, we present a risk theory application in the following scenario: In each period of time we have a change in the capital of the ensurance company and the outcome of a two-state Markov chain stabilishs if the company pays a benece it heat to one of its policyholders or it receives a Hightimes c > 0 paid by someone buying a new policy. At the end we will determine once again by the recursive equation for expectation the time ruin for this company / Neste trabalho, apresentamos uma aplica??o da teoria do risco com o seguinte cen?rio: as mudan?as no capital de uma seguradora acontecem em cada instante de tempo e o pagamento de uma indeniza??o ou recebimento de um pr?mio ? decidido pelo resultado de uma cadeia de Markov de dois estados. Nesta situa??o calculamos a probabilidade de ru?na e o tempo esperado de ru?na quando o valor da indeniza??o ? um m?tiplo do valor do pr?mio

This thesis project revolves around the last days of an abandoned building in decay, facing demolition. It is situated in Värtahamnen, a harbor area in Stockholm. The area is the subject of a major urban planning project in the upcoming decade. In my project my aim is to contemplate this condition of of a building and how to approach and use the ephemerality of architecture and design in the creative process. By extracting different material behaviors caused by decay and exploring them experimentally, a diverse “buffet” of design concepts and methods are presented. The project also orbits around the subject of preservation, a topic commonly debated during interventions in the built heritage. Instead of taking a stand for or against the demolition of the building, the field of experimental preservation is used as a theoretical and methodological background in the design process, as a way to expand the scope on how to navigate and work artistically with preservation. In conclusion, this project tries to revise our perspective on the concept of decay as something destructive and instead suggest the creative potential in understanding it. It also contributes with reflections and speculations on how we can find new creative strategies for taking the whole lifespan of a design project into account already from the beginning.

Dans ce travail nous abordons deux problèmes non résolus en Probabilité appliquée. Nous les approchons tous deux sous un angle nouveau, en utilisant des outils aussi variés que les chaînes de Markov, les mouvements Browniens, les transformations de Schwarz-Christoffel, les processus de Poisson et la théorie des temps d'arrêts optimaux. Problème de la ruine pour N joueurs Le problème de la ruine pour $N$ joueurs est un problème célèbre dont la solution pour $N=2$ est connue depuis longtemps. Nous l'abordons premièrement en toute généralité, en le modélisant comme un problème d'absorption pour une chaîne de Markov. Nous obtenons les distributions associées à ce problème et nous décrivons un algorithme (appelé {it folding algorithm}) permettant de diminuer considérablement le nombre d'opérations nécessaires à une résolution complète. Cette étude nous permet de mettre en avant un certain nombres de relations de récurrence satisfaites par les probabilités de ruines associées à chaque état de la chaîne de Markov. Nous étudions ensuite une version asymptotique du problème de la ruine pour 3 joueurs. Nous utilisons les propriétés d'invariance des mouvements Browniens par transformations conformes pour décrire une résolution de ce problème via les transformations de Schwarz-Christoffel. Cette méthode dépasse le cadre strict du problème de la ruine pour 3 joueurs et s'applique à d'autres problèmes de temps d'atteinte d'un bord par un mouvement Brownien. Problème de Robbins Ce problème s'inscrit dans le cadre de la théorie des temps d'arrêts optimaux. C'est un problème d'analyse séquentielle dans lequel un observateur examine $n$ variables aléatoires indépendantes de manière séquentielle et doit en sélectionner exactement une sans rappel. L'objectif est de déterminer une stratégie qui permette de minimiser le rang moyen de l'observation sélectionnée. Nous décrivons un modèle alternatif de ce problème, dans lequel le décideur observe un nombre aléatoire d'arrivées distribuées suivant un processus de Poisson homogène sur un horizon fixe $t$. Nous prouvons l'existence d'une stratégie optimale pour chaque horizon, et nous montrons que la fonction de perte associée à cette stratégie est uniformément continue sur $R$. Nous décrivons une fonction de perte restreinte qui permet d'obtenir une estimation de la valeur asymptotique du problème, et nous obtenons la valeur asymptotique associée à des stratégies spécifiques. Nous obtenons ensuite une équation intégro-diffférentielle sur la fonction de perte associée à la stratégie optimale. Finalement nous étudions les valeurs asymptotiques du problème et nous les comparons à celles du problème en temps discret. Nous concluons cette thèse en décrivant des stratégies spécifiques qui permettent d'obtenir des estimations sur le comportement asymptotique de la fonction de perte.

Chronologically I have described the different environments that I have been exposed to in the past five years and how my interactions with the different locations have affected my work. I started writing about what I was doing a year after finishing my undergraduate degree, when I started to feel as though I needed to re-invent my work in a way that also meant trying to see the process of creating art differently. I didn't know yet how this new work would begin to generate, or what would inspire it, but I knew that I was seeking a studio practice that would be personal enough to sustain a lifetime of exploration. In the end I found the inspiration had always been all around me.

[pt] Na dissertação cartografa-se distintos modos com que a escrita e, num sentido mais amplo, as artes, se relacionam com a noção de ruína. Parte-se do ponto de tensão entre ruir e criar a fim de explorar o paradoxo de que nos fala Maurice Blanchot em O espaço Literário: a literatura se edifica a partir de suas próprias ruínas. Detendo o gesto cartográfico em uma região particular, tomo algumas obras do escritor e artista visual Nuno Ramos como ocasião favorável para refletir sobre a relação entre destruição e criação na fronteira entre escrita e linguagem visual. O trabalho segue dois eixos que se querem recíprocos, não hierárquicos: no primeiro eixo acentua-se a parte teórico-crítica da pesquisa. No segundo, apresenta-se poemas e outros textos pessoais, escritos que, produzidos ao longo da pesquisa, fazem parte da reflexão. / [en] In this dissertation I cartograph distinct ways in which writing and, in a broader sense, the arts, relate to the notion of ruin. I begin at the point of tension between collapse and creation, to explore the paradox Maurice Blanchot speaks of in The Literary Space: Literature is built upon its own ruins. Holding the cartographic gesture in a particular region, I review works of the writer and visual artist Nuno Ramos as a favorable occasion to reflect on the relationship between destruction and creation on the border between written and visual language. The work follows two reciprocal axes, non-hierarchical: the first axis is emphasizes the theoretical and critical part of the research. In the second, it presents poems and other personal texts, writings produced during the research, and that are part of the reflection.

La presente investigación aborda la novela de fin de siglo XX en Colombia entre 1990 y 2005 desde una orientación panorámica. El estudio se plantea desde el punto de vista de la escritura y se elabora a través del análisis de algunas novelas del periodo a partir de los conceptos mundo, autor, fragmento. Para ello se centra en las novelas Rosario Tijeras de Jorge Franco, Entre fantasmas de Fernando Vallejo, y Pavana del ángel de Roberto Burgos Cantor. Así las cosas el estudio presenta tres capítulos centrales. En la introducción se explica el propósito de la investigación. El primer capítulo trabaja el concepto de mundaneidad en la obra de Rosario Tijeras de Jorge Franco, dialogando con la novela Después de todo de Piedad Bonnett y El anarquista jubilado de Roberto Rubiano. El segundo capítulo intenta delimitar el concepto de autor y la forma como se configura en Entre fantasmas de Fernando Vallejo, para ello se pone en diálogo con Asuntos de un hidalgo disoluto de Héctor Abad Faciolince, Amirbar de Álvaro Mutis, Érase una vez el amor pero tuve que matarlo de Efraim Medina Reyes y Vida feliz de un joven llamado Esteban de Santiago Gamboa. El tercer capítulo analiza el modo como se presenta el fragmento en la novela Pavana del ángel de Roberto Burgos Cantor, novela que se inscribe en la tradición literaria de Colombia y, en particular, del Caribe colombiano. Dicha novela se pone en relación con la novela Opio en las nubes de Rafael Chaparro Madiedo y se relaciona también con la novela Los cuadernos de N. de Nicolás Suescún. Finalmente, en las conclusiones se busca fijar las líneas generales del camino que se ha seguido en esta investigación. / This research studies the romance on the end of the twentieth century in Colombia between 1990 and 2005 in a panoramic orientation. The analysis is approached from the point of view of writing and is made through the analysis of some novels of the period from the concepts of world, author and fragment. This research, also, is focused on the novels Rosario Tijeras by Jorge Franco, Entre fantamas by Fernando Vallejo and Pavana del angel by Roberto Burgos Cantor. On this way, the study presents three chapters; the introduction presents the purpose of the research and its explanation. The first chapter works with the concept of worldliness in the romance Rosario Tijeras by Jorge Franco, in a direct dialogue with the novel Después de todo by Piedad Bonnett and El anarquista jubilado by Roberto Rubiano. The second chapter attempts to define the concept of author and how it is configured in Entre fantasmas by Fernando Vallejo, for that purpose, it is brought into dialogue with Memorias de un hidalgo disoluto by Héctor Abad Faciolince, Amirbar by Alvaro Mutis, Érase una vez el amor pero tuve que matarlo by Efraim Medina Reyes and Vida feliz de un joven llamado Esteban by Santiago Gamboa. The third chapter discusses how the fragment is presented in Pavana del ángel by Roberto Burgos Cantor, a novel that is part of the literary tradition of Colombia and in particular, the Colombian Caribbean. This novel is set in relation to the novel Opio en las nubes by Rafael Chaparro Madiedo and also relates to the romance Los cuadernos de N., by Nicolás Suescún. The conclusion tries to define the way this research was developed.

This thesis presents the results of a multi-disciplinary investigation of a variant Ancestral Pueblo mortuary rite at Wallace Ruin, southwest Colorado (USA). This multi-storey building is one of four Lakeview Group great houses connected to the Pueblo II regional system centred at Pueblo Bonito of Chaco Canyon some 100 km to the south. From c. AD 1060-1150, Wallace Ruin functioned as a ritual-economic centre with a small residential component. Then, habitation of this great house, the Lakeview Group and all domiciles within 10 kilometres ceased. However, three or more decades later at least six rooms were used as a non-residential, Pueblo III mortuary facility for a minimum of 32 individuals. This utilisation was in marked contrast to the enduring Ancestral Pueblo practice of residential burial, usually in the extramural midden. The interrogation of several hypotheses regarding this anomaly entails a bioarchaeological approach that integrates skeletal evidence with spatial analyses regarding diachronic mortuary location choices at Wallace Ruin. Taphonomic methods that segregate bone displacements during corpse decomposition in a filled versus a void space provide accurate determinations of the depositional versus discovered mortuary microenvironments. The diachronic analysis of data from roughly 200 San Juan Region sites reveals additional ways in which Wallace’s Pueblo III mortuary program departs from longstanding communities of practice, whether great house or domicile. Chief among these are the use of a surface room floor and the postural arrangement of supine bodies with knees upright. These results, in combination with material culture evidence, form the basis of this thesis: The Pueblo III mortuary program at Wallace Ruin is a variant rite that entails a Mesa Verde Region reformulation of a Pueblo Bonito house society. The sanctioned retrieval of objects of memory offers a plausible explanation for intentional intrusions into two mortuary contexts. Beyond addressing questions concerning Wallace Ruin, a major contribution of this study includes advancement of the house society model as an interpretive scheme for evaluating Mesa Verde Region socio-ritual dynamics. This research also demonstrates the effectiveness of anthropologie de terrain (Duday, 2006) to retrospectively determine the original status of Ancestral Pueblo mortuary microenvironments. The refinement developed for this study, in which Range of Motion criteria are used to detect large-scale movements of lower limbs during corpse decomposition, is suitable for bioarchaeological analyses the world over.