Research On Several Kinds Of Ruin-Related Problems Under The Risk Model

The risk theory is an important part of insurance and actuarial science,and it occupies a very significant position in the field of finance and insurance.Among which the ruin theory is the core content of the risk theory.This paper mainly studies four kinds of ruin-related problems in the ruin theory,namely,Gerber-Shiu function,the first hitting time,the total duration of negative surplus and the probability of bankruptcy.Finally,numerical examples are used to verify the conclusions.In the first chapter,we mainly introduce the research background of Gerber-Shiu function,the first hitting time,the total duration of negative surplus and the probability of bankruptcy,and give the preliminary knowledge of classical risk model.In the second chapter,the Gerber-Shiu functions of the thinning risk model and the dual risk model are studied.Then the defective renewal equation of the Gerber-Shiu function under the thinning risk model and the integral differential equation of the Gerber-Shiu function under the dual risk model are obtained.Finally,the approximate values and the explicit expressions of the ruin probability are given respectively.In the third chapter,we mainly investigate the first hitting time of the CIR model.Firstly,the LST(Laplace-Stieltjes transform)of the first hitting time is obtained through the strong Markov property of the surplus process and Dynkin’s formula,and then the conclusion is validated by data and some economic analysis is carried out.In the fourth chapter,we mainly consider the total duration of negative surplus under the risk model with credit and debit interests.The LST of the total duration of negative surplus is derived by using the strong Markov property of the surplus process and Dynkin’s formula,and the explicit expression of the LST of the total duration is obtained under the exponential distribution.In the fifth chapter,we mainly study the bankruptcy probability of the risk model with variable premium rates under Omega model.Firstly,the integral differential equation of the bankruptcy probability is derived.Then,numerical examples are given to verify the conclusion,and the comparison between the risk model with variable premium rates and the risk model with constant premium rates is made.