The Ruin Problem Of Insurance Company Based On Hawkes Process

As a crucial component of the insurance system,the insurance company is bound up with the welfare of the society.In the history of the global insurance industry,especially in developed countries,the bankruptcy of insurance companies is not a rare phenomenon,which has brought great adverse effects to the welfare of all citizen in these countries.This paper studies the ruin problem of the insurance company.In the research field of insurance company bankruptcy,it is important to find the theory suitable for the simulation of claims arrival process.The classical model used Poisson process to simulate the claims arrival process,but in fact it is flawed,because in real life,the solvency crisis caused by the infectious risk accident is the main reason for bankruptcy of insurance companies,and the assumption of stationary increment and independent increment has made the Poisson process improper to the simulation of infectious risk and aggregate risk.Compared to the Poisson process,the Hawkes process with its properties that can capture the infectious risk and aggregate risk can be better for the simulaition of claims arrival process.This paper studies the ruin problem of insurance company based on the Hawkes process.From the results of the theoretical model,the insurer's bankruptcy probability is determined by the initial surplus u and the parameters w,while the parameter w decreases as the concentration risk and the contagious risk of the insurance increase.The theoretical bankruptcy probability of the insurer will increase when the initial surplus of the insurance company falls as well.In order to verify the conclusion of the theoretical model,this paper takes Fubin property insurance company as an example to study the influence of the infectious risk and concentration risk on the surplus process of Fubin financial insurance company.Based on the 2011-2015 years' insurance data,estimation loss data and determined data of Fubin financial insurance company,the parameters involved in the theoretical model are fitted,and the Hawkes process is used to simulate the arrival process of the claim event of Fubin property insurance company.We change the value of the parameter 8 of the Hawkes process to study the influence of the collection risk on the surplus process of insurance company.When the insurance claims event occurs centrally,the insurance company is liable to go bankrupt.Therefore,we put forward the policy suggestion:the insurance supervision institution should consider the effect of self-excited of the insurance claims after the external stimulus,that is to consider the potential contagious risk and aggregate risk.In the concrete implementation plan,this paper proposes to add the capital requirements for the risk of concentration in the measurement of the minimum capital of insurance risk,and the characteristics of the risk and concentration risk should be added to the measurement of the minimum capital of insurance risk.