Évaluation des mesures de ruine dans le cadre de modèles avancés de risque

La théorie du risque consiste en l'étude de modèles décrivant le processus de surplus d 'une compagnie d 'assurance. L'évaluation de différentes mesures de ruine dans le cadre de ces modèles permet d'obtenir une idée générale de la santé financière de la compagnie d'assurance et du risque assumé par celle-ci. Le modèle classique de risque pour décrire les arrivées et les coûts des sinistres est le modèle Poisson composé. Ce modèle est basé sur une hypothèse d 'indépendance entre le montant des sinistres et le temps écoulé entre chacun. Cette hypothèse facilite le calcul des mesures de ruine mais peut s'avérer trop restrictive dans différents contextes. L'objectif principal de cette thèse est l'étude d'extensions du modèle classique dans lesquelles sont introduites une structure de dépendance entre la sévérité et la fréquence des sinistres. La copule de Farlie-Gumbel-Morgenstern et une extension de cette copule sont utilisées pour définir cette structure. En raison de la forme et de la flexibilité de ces copules, il est possible d'adapter les outils développés récemment en théorie du risque dans l'évaluation et l'analyse des mesures de ruine. La fonction de Gerber-Shiu et certains cas particuliers de cette fonction , comme la transformée de Laplace du temps de la ruine et l'espérance de la valeur actualisée du déficit à la ruine sont étudiées dans le cadre de ces extensions. On s'intéresse également à l'évolution du processus de surplus en présence d'une barrière horizontale. Les mesures de ruine citées plus haut, ainsi que le montant total actualisé des dividendes distribués sont évaluées.[Copule de Farlie-Gumbel-Morgenstern ; Modèle Poisson composé

On the moments of the aggregate discounted claims with a general dependence

Abstract: Please refer to full text to view abstract

Heat Stroke in Emergency Department: Diagnosis and Management

Background: Heat stroke is a severe health concern with the potential for multi-organ failure, necessitating rapid and effective management. With rising global temperatures, there is increasing concern regarding the vulnerability of populations in high-heat areas, notably in Saudi Arabia, especially during the annual Hajj pilgrimage. Objective: This paper aims to review the epidemiology, evaluation and management techniques of heat stroke, emphasizing the situation during Hajj pilgrimages in Saudi Arabia, and to outline the best practices for emergency management. Methodology: A comprehensive review of literature and studies related to heat stroke, both globally and specific to Saudi Arabia, was undertaken. An in-depth analysis of emergency management, including initial assessment, cooling methods, organ support, medication, and prevention strategies, was conducted. Results: Heat stroke remains a significant cause of emergency department visits, with specific groups, such as men and the elderly, being more susceptible. During the Hajj in 2016, 267 patients were diagnosed with heat-related illnesses, with heatstroke accounting for 29% of these cases. With the threat of global warming, studies indicate a potential tenfold increase in heat stroke risk with a 2°C rise in temperatures. Swift and comprehensive cooling is pivotal for recovery. Management emphasizes rapid recognition, assessment, and varied cooling methods, along with targeted treatments for organ dysfunctions. Prevention strategies play a vital role, given the higher efficacy and practicality over treating organ dysfunctions. Conclusion: Heat stroke is a pressing health challenge, particularly in high-risk environments like Saudi Arabia during the Hajj pilgrimage. While effective emergency management protocols exist, an emphasis on prevention is crucial. It is imperative to incorporate a comprehensive approach to address both the immediate threat and long-term risks of heat stroke, especially with the looming challenge of global warming

Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models

In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims

On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula

In this paper we consider an extension to the classical compound Poisson risk model in which we introduce a dependence structure between the claim amounts and the interclaim time. This structure is embedded via a generalized Farlie-Gumbel-Morgenstern copula. In this framework, we derive the Laplace transform of the Gerber-Shiu discounted penalty function. An explicit expression for the Laplace transform of the time of ruin is given for exponential claim sizes.Compound Poisson risk model Copula Generalized Farlie-Gumbel-Morgenstern copulas Ruin theory Dependence models Gerber-Shiu discounted penalty function