As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

This thesis examines stabilizing mechanisms in social security retirement systems (“SSRS”), especially those purporting to be automatic balancing mechanisms (“ABM”). It develops a consistent approach to identifying whether an ABM is robust, partial or transitory and establishes a terminology to classify balancing mechanisms. Both financial and equitable balances are considered in assessing whether an ABM achieves balance. Families of definitions of equity are presented and a benchmark by which to measure equitable balance is defined and applied. The balancing mechanisms of Canada, Germany, Japan and Sweden are described, evaluated and classified. None of these mechanisms are found to be robust. This thesis provides a critical analysis of an approach referred to as integration to financial markets and the approach is found to be deficient. In analyzing the Swedish SSRS a critical error in the way assets are calculated is identified and a suitable correction is proposed. A further weakness in the application of the Swedish ABM is identified that means that once an imbalance occurs, balance is unlikely to be restored. The thesis also discusses some of the unusual characteristics of the steady-state contribution rate calculation for the Canadian SSRS and shows that although it has limited application and does not appear to depend on any actuarial principle, the steady-state contribution rate calculation creates a tension between the near and distant future, which is a factor in achieving financial balance over a seventy-five year horizon. With respect to the balancing mechanism in the Canadian SSRS, the thesis proposes a change in how the mechanism is defined so that the mechanism would be robust, within certain ranges.

As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

This thesis examines stabilizing mechanisms in social security retirement systems (“SSRS”), especially those purporting to be automatic balancing mechanisms (“ABM”). It develops a consistent approach to identifying whether an ABM is robust, partial or transitory and establishes a terminology to classify balancing mechanisms. Both financial and equitable balances are considered in assessing whether an ABM achieves balance. Families of definitions of equity are presented and a benchmark by which to measure equitable balance is defined and applied. The balancing mechanisms of Canada, Germany, Japan and Sweden are described, evaluated and classified. None of these mechanisms are found to be robust. This thesis provides a critical analysis of an approach referred to as integration to financial markets and the approach is found to be deficient. In analyzing the Swedish SSRS a critical error in the way assets are calculated is identified and a suitable correction is proposed. A further weakness in the application of the Swedish ABM is identified that means that once an imbalance occurs, balance is unlikely to be restored. The thesis also discusses some of the unusual characteristics of the steady-state contribution rate calculation for the Canadian SSRS and shows that although it has limited application and does not appear to depend on any actuarial principle, the steady-state contribution rate calculation creates a tension between the near and distant future, which is a factor in achieving financial balance over a seventy-five year horizon. With respect to the balancing mechanism in the Canadian SSRS, the thesis proposes a change in how the mechanism is defined so that the mechanism would be robust, within certain ranges.

Depuis longtemps les modèles de type phase sont utilisés dans plusieurs domaines scientifiques pour décrire des systèmes qui peuvent être caractérisés par différents états. Les modèles sont bien connus en théorie des files d’attentes, en économie et en assurance.<p><p>La thèse est focalisée sur différentes applications des modèles de type phase en assurance et montre leurs avantages. En particulier, le modèle de Lin et Liu en 2007 est intéressant, parce qu’il décrit le processus de vieillissement de l’organisme humain. La durée de vie d’un individu suit une loi de type phase et les états de ce modèle représentent des états de santé. Le fait que le modèle prévoit la connexion entre les états de santé et l’âge de l’individu le rend très utile en assurance.<p><p>Les résultats principaux de la thèse sont des nouveaux modèles et méthodes en assurance pension et en assurance santé qui utilisent l’hypothèse de la loi de type phase pour décrire la durée de vie d’un individu.<p><p>En assurance pension le but d’estimer la profitabilité d’un fonds de pension. Pour cette raison, on construit un modèle « profit-test » qui demande la modélisation de plusieurs caractéristiques. On décrit l’évolution des participants du fonds en adaptant le modèle du vieillissement aux causes multiples de sortie. L’estimation des profits futurs exige qu’on détermine les valeurs des cotisations pour chaque état de santé, ainsi que l’ancienneté et l’état de santé initial pour chaque participant. Cela nous permet d’obtenir la distribution de profits futurs et de développer des méthodes pour estimer les risques de longevité et de changements de marché. De plus, on suppose que la diminution des taux de mortalité pour les pensionnés influence les profits futurs plus que pour les participants actifs. C’est pourquoi, pour évaluer l’impact de changement de santé sur la profitabilité, on modélise séparément les profits venant des pensionnés.<p><p>En assurance santé, on utilise le modèle de type phase pour calculer la distribution de la valeur actualisée des coûts futurs de santé. On développe des algorithmes récursifs qui permettent d’évaluer la distribution au cours d’une période courte, en utilisant des modèles fluides en temps continu, et pendant toute la durée de vie de l’individu, en construisant des modèles en temps discret. Les trois modèles en temps discret correspondent à des hypothèses différentes qu’on fait pour les coûts: dans le premier modèle on suppose que les coûts de santé sont indépendants et identiquement distribués et ne dépendent pas du vieillissement de l’individu; dans les deux autres modèles on suppose que les coûts dépendent de son état de santé.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished