Rersearch On Ruin Probability Of Dependent Risk Model With Random Premium

In recent years,bankruptcy theory has received more and more attention.Studying bankruptcy theory is useful for insurance companies to make predictions about the future and avoid risks in a timely manner.It has important practical significance.Numerous experts and scholars have conducted extensive research on the basis of Lundberg-Cramer's classic bankruptcy theory.In previous studies,claims counting processes from different businesses were mostly independent,with fewer dependent structures.Therefore,this paper studies the probability of bankruptcy for a dependent risk model with random premiums.The main structure as follows:In chapter 1,we briefly analyzes the background of risk theory and its latest research trends.Then,the main content of this paper is introduced.In chapter 2,we mainly introduces the classical risk model,some distributions,dependencies and some basic knowledge of stochastic process.In chapter 3,we study the ruin probability based on the constant interest rate dependent risk model.In this model,it is assumed that the size of claims from the same business is heavy-tailed,and the upper tail is asymptotically independent.The arrival process of different business claims is positively quadrant dependent or arbitrarily dependent.we use limit theory and random analysis methods to obtain ruin probability uniform asymptotic formula.In chapter 4,we mainly study the ruin probability of a dependent risk model with stochastic premium.In this model,the counting process corresponding to premium income and claim arrival process are Poisson process.Here,we assume that premium income arrival processes from different businesses are dependent due to public shocks,The claim arrival processes are dependent on the same counting process.The claim size distribution from the same business is independent and the same distribution.Using the property of martingale,we get the upper bound of the Lundberg type ruin probability.