In life insurance contracts, actuaries generally value premiums using deterministic mortality rates and interest rates. They have ignored them stochastically in most of the studies. However it is known that neither interest rates nor mortality rates are constant. It is also known that companies may encounter insolvency problems such as ruin, so the ruin probability need to be added to the valuation of the life insurance contracts process. Insurance companies should model their surplus processes to price some types of life insurance contracts and to see risk position. In this study, mortality rates and surplus processes are modeled and financial strength of companies are utilized when pricing life insurance contracts.

In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some characteristics of the renewal equation are assumed to have non-polynomial perturbations, more specifically they can be expanded with respect to a non-polynomial asymptotic scale. The main result of the present study is exponential asymptotic expansions for the solution of the perturbed renewal equation. These asymptotic results are also applied to various applied probability models like perturbed risk processes, perturbed M/G/1 queues and perturbed dam/storage processes. The thesis is based on five papers where the model described above is successively studied.

Ce travail de thèse porte principalement sur deux problématiques différentes mais qui ont pour point commun, la contribution à la modélisation et à la gestion du risque en actuariat. Dans le premier thème de recherche abordé dans cette thèse, on s'intéresse à la modélisation de la dépendance en assurance et en particulier, on propose une extension des modèles à facteurs communs qui sont utilisés en assurance. Dans le deuxième thème de recherche, on considère les distributions discrètes décroissantes et on s'intéresse à l'étude de l'effet de l'ajout de la contrainte de convexité sur les extrema convexes. Des applications en liaison avec la théorie de la ruine motivent notre intérêt pour ce sujet. Dans la première partie de la thèse, on considère un modèle de risque en temps discret dans lequel les variables aléatoires sont dépendantes mais conditionnellement indépendantes par rapport à un facteur commun. Dans ce cadre de dépendance on introduit un nouveau concept pour la modélisation de la dépendance temporelle entre les risques d'un portefeuille d'assurance. En effet, notre modélisation inclut des processus de mémoire non bornée. Plus précisément, le conditionnement se fait par rapport à un vecteur aléatoire de longueur variable au cours du temps. Sous des conditions de mélange du facteur et d'une structure de mélange conditionnel, nous avons obtenu des propriétés de mélanges pour les processus non conditionnels. Avec ces résultats on peut obtenir des propriétés asymptotiques intéressantes. On note que dans notre étude asymptotique c'est plutôt le temps qui tend vers l'infini que le nombre de risques. On donne des résultats asymptotiques pour le processus agrégé, ce qui permet de donner une approximation du risque d'une compagnie d'assurance lorsque le temps tend vers l'infini. La deuxième partie de la thèse porte sur l'effet de la contrainte de convexité sur les extrema convexes dans la classe des distributions discrètes dont les fonctions de masse de probabilité (f.m.p.) sont décroissantes sur un support fini. Les extrema convexes dans cette classe de distributions sont bien connus. Notre but est de souligner comment les contraintes de forme supplémentaires de type convexité modifient ces extrema. Deux cas sont considérés : la f.m.p. est globalement convexe sur N et la f.m.p. est convexe seulement à partir d'un point positif donné. Les extrema convexes correspondants sont calculés en utilisant de simples propriétés de croisement entre deux distributions. Plusieurs illustrations en théorie de la ruine sont présentées / In this thesis we focus on two different problems which have as common point the contribution to the modeling and to the risk management in insurance. In the first research theme, we are interested by the modeling of the dependence in insurance. In particular we propose an extension to model with common factor. In the second research theme we consider the class of nonincreasing discrete distributions and we are interested in studying the effect of additional constraint of convexity on the convex extrema. Some applications in ruin theory motivate our interest to this subject. The first part of this thesis is concerned with factor models for the modeling of the dependency in insurance. An interesting property of these models is that the random variables are conditionally independent with respect to a factor. We propose a new model in which the conditioning is with respect to the entire memory of the factor. In this case we give some mixing properties of risk process under conditions related to the mixing properties of the factor process and to the conditional mixing risk process. The law of the sum of random variables has a great interest in actuarial science. Therefore we give some conditions under which the law of the aggregated process converges to a normal distribution. In the second part of the thesis we consider the class of discrete distributions whose probability mass functions (p.m.f.) are nonincreasing on a finite support. Convex extrema in that class of distributions are well-known. Our purpose is to point out how additional shape constraints of convexity type modify these extrema. Two cases are considered : the p.m.f. is globally convex on N or it is convex only from a given positive point. The corresponding convex extrema are derived by using a simple crossing property between two distributions. Several applications to some ruin problems are presented for illustration

This thesis analyzes the current settings of occupational health and safety process regarding officers of the Municipal Police of Prague (MPP). The theoretical part provides situational analysis of conditions in which MPP operates. There are also defined key risks for personal safety of municipal policemen, identified methodology for risk management and quality control. The practical part describes and analyzes the process of occupational health and safety at MPP. The result of this work is evaluation of the current process effectiveness and proposal of possible scenarios of further improvement.

In this thesis, nonlinearly perturbed stochastic models in discrete time are considered. We give algorithms for construction of asymptotic expansions with respect to the perturbation parameter for various quantities of interest. In particular, asymptotic expansions are given for solutions of renewal equations, quasi-stationary distributions for semi-Markov processes, and ruin probabilities for risk processes. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.</p>

Titel: Riskhantering av molnbaserade affärssystem Författare: Fredrik Forsberg &amp; Kevin Adamsson Handledare: Pia Nylinder Examinator: Petter Boye Kurs: Företagsekonomi, Kandidatuppsats inom ekonomistyrning/redovisning Kurskod: 2FE75E Frågeställning: Hur arbetar företag inom bilförsäljningsbranschen med riskhanteringen av molnbaserade affärssystem? Syfte: Studiens syfte är att undersöka vilka risker molnbaserade affärssystem medför och hur företag inom bilhandeln arbetar för att hantera riskerna. Metod: För att uppfylla studiens mål har vi använt oss av den abduktiva ansatsen. Semistrukturerade intervjuer har genomförts och vi har genom detta samlat in empiri från åtta olika respondenter som är verksamma inom bilhandeln. Slutsats: Vi har kommit fram till att storleken på företag har en stor påverkan på hur riskprocessen samt riskhanteringen sker, även om riskerna har samma prioriteringsnivå. De flesta företagen har en plan för hur de skall hantera riskerna och arbeta för att motverka dessa. Vi har även kommit fram till att större ekonomiska resurser ger större utrymme för att arbeta i förebyggande syfte och på så sätt motverka de riskerna som studien har handlat om. Nyckelord: molntjänster, molnbaserade affärssystem, risker med molnbaserade affärssystem, riskhantering i samband med molnbaserade affärssystem, riskprocess. / Title: Risk management of cloud-based ERP-systems Writers: Fredrik Forsberg &amp; Kevin Adamsson Supervisor: Pia Nylinder Examiner: Petter Boye Course: Business administration, Bachelor thesis in finance/accounting Course code: 2FE75E Research question: How do companies in the automotive trade industry work with risk management of cloud-based ERP-systems? Purpose: The purpose of this paper is to examine what risks that the cloud based ERP-systems entail and how companies in the automobile trade work with the risk management. Method: To fulfill the purpose of this paper we have used the abductive approach. Semi-structured interviews have been conducted in order to retrieve empirical data from eight different respondents who operates in the automobile trade. Conclusion: We have come to the conclusion that the size of the companies has a major impact on how the risk process and the risk management are done, even if the risks have the same level of priority. Greater financial resources provides more space for the companies to work with the risk management. Keywords: Cloud based services, Cloud based ERP-system, Risks with the cloud based ERP-systems, Risk management, Risk process.

The first part of my work is focused on technology of Oracle. Here are mentioned individual languages, which works with data and different data types. Here is made clear manner, how are data saved in the database. Next I described technology of Apollo, on which information system Apollo is build. Next part of my work is analyze, in which is described present state of evaluation risk process and requests, which are layed on this module. Following chapter is implementation. There are described both database schema and by detail parts of module in a form of strips. Here is at large interpreted the way how to value risk and risk process. This chapter contains print reports for this module as well. The next chapter is dedicated to how module was brought to functioning. Except making this module running in information system Apollo is here a chapter about education of employees. In the closure I present evaluation of reached results, show next development and present my own benefit.

We derive formulas for the moments of the ruin time in a Lévy risk model and use these to determine the asymptotic behavior of the moments of the ruin time as the initial capital tends to infinity. In the special case of the perturbed Cramér-Lundberg model with phase-type or even exponentially distributed claims, we explicitly compute the first two moments of the ruin time. All our considerations distinguish between the profitable and the unprofitable setting.