A Double Type-insurance Risk Model With Random Premium And Constant Interest

In this thesis, we study a kind of double type-insurance risk model with randompremium, random premium income and two classes of claims may happen under constantinterest. The contents and structures of the dissertation are organized as follows:In Chapter1, firstly, we introduce the basic knowledge related with this thesis.Furthermore, a double type-insurance risk model with random premium and constantinterest is introduced. Finally, the known results of this model are given in specialcircumstances.In Chapter2, using recursive method, we study some common distributions ofactuarial index of this model. Such as the ruin probability, the survival probability, thesurplus immediately before ruin, deficit at ruin, the supremum surplus before ruin inclaim moment, as well as the supremum surplus and minimum surplus before ruindistribution, the joint distribution functions of the surplus immediately before ruin anddeficit at ruin, the joint distribution functions of the surplus immediately before ruin, thedeficit at ruin and the maximum surplus on claim moment before ruin.In Chapter3, further, we study some complex actuarial index of this model. Firstly,the integral equations of the duration of ruin and distribution of the moment when thesurplus for the first time through an assigned level at claim moment are given; Secondly,the Gerber-Shiu expected discounted penalty function and some description insurancecompany bankrupt actuarial index integral equations in special situations are discussed.Finally, the integral equations of the tail probability of deficit, the functional inequality ofthe tail probability of deficit and some exponential upper bounds of the tail probability ofdeficit are obtained. In Chapter4, we summarize the thesis and point out what we will do based on thisthesis.