Study Of The Continuous-time Dependent Risk Model's Ruin Probability

In classical risk model and many extended risk models, the independence property of random variables is an important assumption. In practice, however, this assumption is too idealized. There are certain correlations between classes of business because common factor which cause risk exists, thus comparing with the classical risk model, it is more realistic to consider dependent risk models. In this thesis, we construct and research four kinds of dependent risk models, and we obtain some results about the ruin probability with the knowledge of probability and random process, it contains:(1)The bivariate risk model with independent claim point processes is extended to dependent claim point processes, and the limit of ruin is extended to the function f(t) from zero. By converting the risk model, we obtain the ultimate ruin probability of the risk model.(2)Considering the bivariate risk model with dependent claim point processes which is perturbed by diffusion, and popularize the claim point process into Cox process, we offer the super bound of ultimate ruin probability with the martingale method.(3)Discussing the risk model which the claim point process and the re-premium point process are correlated under the thinning process, we obtained some properties of the profit process and the survival probability.(4)Studying the risk model which the premium point process and the claim point process are correlated in the form of common shock, by converting the risk model, we obtain the integral representation of the ultimate non-ruin probability and the integral-differential representation of the finite non-ruin probability when the intensity process of the Cox process is a Markov jump process.