Several Classes Of Markov Modulated Dual Risk Model With Research

In this thesis, we construct several kinds of double-type risk models in view of the generalization of premiums income process, claims arrival process and the shortage of the classical risk models.In the third chapter, we mainly discuss a kind of double-type risk model that premiums income process is modulated by a Markov process. Premium income process of the classical model is generalized to a markov-modulated premium income, and one-type risk model is generalized to double-type risk model. A integral equation for the conditional ruin probability is obtained under the given initial states. Furthermore, a recursive inequality of the ruin probability with the stationary initial distribution and a simplified estimation of ruin probability with no initial reserve are given.In the forth chapter, a kind of double-type risk model is introduced. In this case, the premium rate varies with the level of free reserves and the occurrence of claims is described by a Cox process, and the intensity process of the Cox process is a homogeneous n-state Markov process. An integral equation of the conditional ruin probability is obtained under the given initial states of the markov processes .So an integral equation is obtained for the 0 initial capital. Furthermore, the ruin probability with the stationary initial distribution is given.In the fifth chapter, we discuss another kind of double-type risk model that for each type insurance product premium rate varies according to the intensity of claims and the occurrence of claims being described by a Cox process and the intensity process of the Cox process is a general jump process. Using backward argument and the Markov property of the intensity process, we obtain the integral equations satisfied by survival probability. Furthermore, the survival probability with the stationary initial distribution is given.