The Research Of A Correlated Claims Risk Model

Risk theory is the quantitative analysis theory of a variety of risks which insurance industry has to face, it is an important subject in actuarial science. In the classical risk theory, the assumption of independence between classes of business is always made in all insurance companies, this is mainly for the convenience of mathematical calculation. However, in real economy life, we often encounter the situation that there are certain correlations between the individual risks , so it is more realistic to consider dependent risk models .The paper introduces the development history of the risk theory,the extension of the classical risk model and the present research on the correlated risk model.The main work in this paper is as follows: Based on some scholars'results, we have considered a widely used count-correlated claims risk model in continuous time situation and discussed the model. It contains two claims which are main claims and by-claims. It is assumed that every main claim may produce a by-claim. An integro-differential equation for the survival probability of the model are obtained with the Complete probability formula and Taylor'sformula, and explicit expressions for the survival probability are given in the case of exponential claims.After that we have made further research on the model and changed the relationship between the main claim and the by-claim and introduced threshold to the risk model.When the main claim is greater than the threshold,the risk model will produce a by-claim, and the by-claim may be delayed. Then we have got the calculation formula for the survival probability when the claims are in the general distribution by laplace transform. And we have also got explicit expressions for the survival probability is given in the case of exponential claims.