The Generalization Of The Classical Risk Process And The Research Of The Generalized Brownian Sheet

Since the classical risk model was established by Lundberg and Cramer, many scholars have already improved and generalized it and a lot of results with respect to the ruin probability have been obtained. In this paper, based on the results which have been gotten, the classical risk model is generalized in some cases, and the properties of their ruin probability are studied. The first generalization is that the premium process is generalized from time determinant function to compound Poisson process. The integral representations of the non-ruin probability are studied, then the Lundberg inequality and the common formula to the ruin probability are shown. The explicit formula of the nonruin probability is obtained in the special case. The second is that the premium process and aggregate claim process are generalized simultaneously to the generalized compound Poisson process on the condition of diffussion perturbing. We may solve practical problem which there are more than two insurance policies and more than two claims at the same time. Also the Lundberg inequality and the common formula for the ruin probability hold in our model by the aid of a martingale approach.We take advantage sufficiently of the current references results in the second part of the thesis (i.e. Chapter 3). In respect to the generalized Brownian sheet, single point Markov properties, relaxed past Markov properties, relaxed future Markov properties and *-Markov properties are discussed. The transition probability and forecasting of the generalized Brownian sheet are also studied.