| Ruin theory,as the focus of risk theory research,is of great significance to the safe operation of insurance companies.The research object of this dissertation is the risk model based on entrance processes(LiM),which was introduced by Li Zehui(2005),and this model is a generalization of the classical risk model from a more practical perspective.On the basis of the previous research results,the thesis extends LiM from two aspects in the previous achievements.On the one hand,we put LiM in a financial cnviromnerit,discuss LiM with the risky investment,and have a comprehensive promotion for the risk model extending claims from independent to dependent,entrance processes from a Poisson process to the update process and the counting process,and heavy-tailed classes from smaller to larger;On the other hand,the single insurance is extended to double insurance.Then,according to whether the two insurance is independent or has some dependence,it carries out classification and get different results.Although some ideas of classical risk model can be used for reference in our research,LiM is a random sum of stochastic processes and a more complex derivation process than the classical risk process is an important work in this paper.The content of this thesis is divided into six chapters.The first chapter introduces the development process and current.situation of the classical model and LiM.In the second chapter,some concepts of dependency,and their relations are introduced.At the same time,some concepts of heavy-tailed distribution families,and their relations are also introduced.The third chapter studies LiM of risky investment with Brown motion.Under the assumption that the claims sizes are pairwise strong quasi-asymptotically inde-pendent,which belong to the classes D and ￡∩D,the upper and lower bounds of the ruin probabilities for finite time and infinite time are obtained,respectively.In particular,the asymptotic expressions for finite time and infinite time are obtained when claims sizes belong to the class C.The fourth chapter studies the two-dimensional independent LiM.Under the assumptions that the entry process of policies of two kinds of business of insurance companies have different.renewal processes,the claims sizes of two kinds of business are independent of each other,and the claims sizes of the same kind of business are pairwise strong quasi-asymptotically independent,which belong to the class ￡∩D,the maximum finite-time ruin probability and the minimum finite-time ruin probability are obtained,respectively.If intervals of entry time of the policy satisfy the wide lower quadrant dependence,The finite-time maximum ruin probability and the finite-time minimum ruin probability are also obtained.The fifth chapter considers the two-dimensional dependent LiM.Under the as-sumptions that the entry process of policies of two kinds of business of insurance companies share the same renewal processes,the corresponding claims sizes of two kinds of business follow a common bivariate Farlie-Gumbel-Morgenstern distribu-tion,and the,claims sizes of the same kind of business are independent,which belong to the class S,the maximum finite-time ruin probability is obtained.The sixth chapter summarizes the full text and forecasts the next phase of the research work. |
