Research On The Ruin Problem Of Dependent Risk Model Based On Erlang(2) Distribution

Risk theory has always been an important part of the research in the insurance industry.It plays an important role in predicting the ruin probability and avoiding the ruin risk of insurance companies.In recent years,more and more attention has been paid to the ruin risk model with dependent structures.In this thesis two types of dependent risk models are considered based on the Erlang(2)distribution.The first model assumes that the conditional distribution of the claim amount is a mixture of any two distributions,and the second model determines the subsequent claim amount by comparing the claim interval with a random threshold.For these two types of dependent models,the Gerber-Shiu penalty function is taken as the research object,and the related ruin problems are studied.This thesis is mainly divided into three chapters.The first chapter is the introduction.It proposes the background of this thesis including the research status of domestic and foreign scholars in the field of insurance claims,several forms of dependent risk model,and briefly introduces the main work of this thesis.In the second chapter,it is assumed that the claim interval is Erlang(2)distribution,and the conditional distribution of the claim amount under the claim interval is a mixture of any two distributions.In section 1,the thesis gives the basic structure of the model.Then in section 2,we use Rouché theorem to study the roots of Lundberg equation.The explicit expression of the Laplace transform of the Gerber-Shiu penalty function is obtained in section3 and the defective renewal equation satisfied by the penalty function is given in section 4.Numerical analysis is given in Section 5.In the third chapter,it is assumed that the threshold is an Erlang(2)distribution.The subsequent claim amount is determined by comparing the claim interval time with the threshold.The thesis gives the basic structure of the model in Section 1.In Section 2,we derive the roots of Lundberg equation.We obtain the integro-differential equation for the Gerber-Shiu penalty function in section 3.In Section 4,we obtain the analytical expression of the Laplace transform of the penalty function,and in Section 5,the structural equation satisfied by the penalty function under the condition of zero initial value is given.Then the defective renewal equation satisfied by the penalty function is derived in Section 6.Finally in Section 7,we make a numerical analysis.