Research On Tail Probability Of Non-standardized Risk Model Based On Dependence Structures

Insurance risk theory mainly applies the relevant knowledge in probability statistics to solve the risk measurement problems in insurance business,and ruin theory is one of its core elements,and risk tail probability is an important form of ruin theory.Insurance plays an important role in the development of the national economy.With the increasing complexity of risk factors in the modern insurance market,the control of insurance risks has brought new challenges.The inability of insurance companies to bear the relevant risks will inevitably have a serious impact on society.By studying the tail probability of the risk model,the corresponding ruin probability can be further deduced,so as to measure the overall risk of an insurance company,which helps the company to make appropriate decisions in a complex environment.In the early financial insurance research,various elements in the research object were usually regarded as independent and identically distributed random variables.But that’s not the case in reality,and there are often some interdependent relationships among them.In recent years,many researchers have found that the risk model includes delayed claims is a more realistic scenario.For example,after a car accident,the insurance company not only has to pay for the loss of the insured’s vehicle,but also the loss of the third party after a period of time if the insured has also purchased third party insurance.Therefore,the study of the thesis is mainly based on the non-standardized risk model with dependence structures,in which each main claim is accompanied by a delayed claim.Due to the complexity of today’s environment,risk models need to consider more factors,such as investment returns,diffusion disturbance terms,dependencies and so on.Especially in risk models involving delayed claims,the dependencies of random variables mostly cannot be described by a single dependence structure.Multiple dependency structures need to be considered,such as possible dependencies between the main claims and their inter-arrival times,the delayed claims and their delayed times,the main claims and the delayed claims,and evenwithin the claim amount sequence.The Sarmanov dependence distribution between claims and their inter-arrival times is considered in the thesis.For the relationship between the main claims and the delayed claims,quasi-asymptotically independent(QAI)dependence structure is considered to describe it.In addition,a onesided linear process is introduced to portray the sequence of main claims.In order to make the model conform to the insurance reality as much as possible,the general adaptive c`adl`ag process is chosen as the stochastic investment returns,and a stochastic disturbance term is added to the model to represent the additional uncertainty factor of the total claim amount or premium income of the insurance company.The asymptotic upper and lower bounds for the tail probability of this risk model are derived,and based on this,the asymptotic results for the ruin probability of the model are further investigated accordingly.Finally,in order to verify the accuracy of the research results,the crude Monte Carlo(CMC)method is used to conduct numerical simulation experiments.