Multi-risk Model With The Two Types Of Income

The risk theory is the basic discipline of learning financial mathematics and the actuarial mathematics of insurance and its core is the study of the ruin theory. In this text, based on the classical risk model ,we construct and research two kinds of new risk models with return. Finally we obtain some expressions or characters of the variables about ruin.Four chapters constitute this text.In the first chapter, we simply introduce the history, the present conditions of the risk theory and the main result, and we especially pay more attention on the classical risk model .finally we present the main content of this text and the main result of my research.In the second chapter , we outline the knowledge about expectation, point process, martingale, Ito's formula and Brownian motion. This knowledge is also the foundation of the text.In the third chapter, we point out the location of the classical risk model, and then construct a new double-multiple risk model with interest force. We analyze and discuss the new model. Finally we attain the integral equations of the non-ruin probability, the immediate distribution before ruin and the deficit distribution at the time of ruin; by the way we present the recursive equations of the immediate distribution before ruin and the surplus distribution at the time of ruin.In the fourth chapter, we point out the deficiency of the model which we construct in the third section, then construct a new multiple risk model with stochastic return on investments. Then we analyze and discuss this model by the Ito's formula and other mathematical tools, and finally present the integral equations and integral-differential equations of the non-ruin probability, the supremum distribution before ruin, and the surplus distribution at the time of ruin...