Progressive Research On The Ruin Probability Of Multidimensional Risk Model

This thesis is mainly to carry out mathematical modeling and theoretical exploration of the bankruptcy problem of insurance companies.The similar mathematical model is a risk model.Based on the requirements of the real problems of insurance company’s practical and the risk of bankruptcy to explore the theoretical knowledge of insurance,this thesis simulates an insurance company with multiple businesses in parallel,and establishes a multi-dimensional risk.Insurance model,to study the ruin probability of the model under certain conditions(i.e.,the total income of the insurance company for the first time is negative probability)and the asymptotic expression for deriving the probability of ruin.The following introduces the main research of this thesis two parts of the study(model):The first model: a two-dimensional risk model with claim relevance and delay time.This model unlike many two-dimensional studies that only study a single factor(claim-related or delayed),in the two-dimensional model,the superposition of two factors(claim correlation and delay time)on the probability of ruin is studied.And successfully deduced the asymptotic formula of the ruin probability of the model.Compared with other models,this model can be more suitable for realistic insurance companies and provide theoretical guidance for insurance companies.The second model: Multi-dimensional risk model with Brownian disturbance.At present,most of the papers that consider disturbance terms are onedimensional or two-dimensional models,and seldom consider three-dimensional Brownian perturbation models with arbitrary correlation counting processes and dependent structures.Therefore,this thesis mainly explores two conditions(1.Different the business claim counting process is arbitrarily related;2.The interval time of arrival of each business has a dependent structure)the influence of the lower Brownian disturbance on this model and its ruin probability.Through the use of mathematical analysis,the knowledge of stochastic process and the method of proof have successfully broken this model.It is also proved that the addition of Brownian perturbation has no effect on the asymptotic result of the ruin probability of the model.