Several Types Of Discrete Risk Model

The classical risk model in fully discrete setting has been studied extensively. However, because of some defects, many scholars generalized it from various aspects. Based on the existent conclusions, the thesis discusses several kinds of discrete risk models from different viewpoints.(1) Single-type risk model in discrete setting. Two special types of this model are discussed in chapter 3. Firstly, considering the actual operation of the insurance company, different unit of time for the policy is usually a random variable, making the arrival of term policies and the occurrence of claims two independent binomial processes, thus the double binomial risk model is obtained. Secondly, we discuss Multinomial distribution risk model, mainly study the recursive formula of Trinomial distribution risk model under arbitral surplus. Based on them, the improved recursive formula to the ultimate ruin probability is deduced. And the algorithm is implemented with Matlab. In case analysis, the improved recursive formula has been validated by comparing the data of the two algorithms obtained.(2) Double-type risk model in discrete setting. This model is discussed in chapter 4. At the beginning, generalize the classical risk model, using general point process to describe the two claim number processes. It is the simplest double-type risk model. The survival probability for arbitral surplus u and the ruin probability for surplus u=0 have been discussed. Additionally, we give the premium income and the claim number further generalization. Hence the generalized double-type risk model is got. The formulas of the ultimate ruin probability and Lundberg inequality are obtained by the use of martingale. In a special situation, we give upper bounds of the finite-time ruin probability.(3) The discrete time correlated multi-type risk model. We study this model in chapter 5. The models where the claim number distributions satisfy Poisson process (PCS model) and NB process (NBCC model) are discussed explicitly, and the corresponding characteristic functions of aggregate claims are given under the two models. Considered the risk processes with two classes of business, PCS model and NBCC model are discussed from two aspects: (1) The impact of the dependence relation on calculation of the premium; (2) Comparing the Lundberg exponents for independence model and dependence model, finally it reflects the impact of the dependence relation on the ruin probabilities. And confirm the conclusion accuracy with example.