A Class Of Delayed And Perturbed Risk Model With Dependence

Insurance companies manage a large amount of funds.If the ruin risk cannot be correctly estimated,it may lead to serious financial consequences.The ruin theory can provide an effective tool for managers.The actuarial theory researchers have built various models to study and predict the possible ruin time,ruin probability,ruin deficit and other risk indicators.In this thesis,we consider a class of delayed and perturbed risk model with dependence,and take Gerber-Shiu discounted penalty function(referred to as Gerber-Shiu function)as the object to study the relevant ruin risk problems.This thesis is divided into three chapters.The main research structure is as follows:The first chapter is the introduction.First,the research background and significance of this thesis are introduced,then the relevant research status at home and abroad are introduced,and finally the main work of this thesis is introduced.In chapter 2,the first-order delayed and perturbed risk model with dependence are studied.In section 1,the structure of the risk model and two Gerber-Shiu functions under ruin caused by claims and oscillations are introduced;In section 2,the Lundberg equation and its roots are studied;In section 3,the integro-differential equations satisfied by two Gerber-Shiu functions are calculated;In section 4,the Laplace transforms satisfied by two Gerber-Shiu functions are calculated;In section 5,the defective renewal equations are obtained according to Lagrange interpolation theorem;In section 6,numerical examples are given.In chapter 3,the second-order delayed and perturbed risk model with dependence are studied.In section 1,the structure of the risk model is introduced.In section 2,the Lundberg equation and its roots are studied;In section 3,the integro-differential equations satisfied by two Gerber-Shiu functions are calculated;In section 4,the Laplace transforms satisfied by two Gerber-Shiu functions are calculated;In section 5,the defective renewal equations are obtained according to Lagrange interpolation theorem;In section 6,numerical examples are given.