Ruin Problems On Two Kinds Of Risk Models

It is well known that the classical risk model is an important stochastic process with properties of temporal homogeneity and independent increment. The study on this model is nearly perfect and exact calculated results for all actuarial diagnostics are derived in analytical form. In this dissertation, we consider several different risk models, including continuous-time compound binomial risk model, continuous-time compound binomial risk model in a Markovian environment, compound binomial-Poisson model and classical risk model that is perturbed by diffusion. We mainly discuss some properties of ruin probability and expected discounted penalty function for the continuous-time compound binomial risk model; Lundberg bounds and Cramer-Lundberg approximations for the continuous-time compound binomial risk model in a Markovian environment and the compound binomial-Poisson model; some measures of the severity of ruin in the classical risk model.The dissertation is consist of six parts: (1) Introduction; (2) Continuous-time compound binomial risk model; (3) Expected discounted penalty function for the continuous-time compound binomial risk model; (4) Continuous-time compound binomial risk model in a Markovian environment; (5) Compound binomial-Poisson model; (6) Some measures of the serverity of ruin in the classical risk model.A brief review of the background of risk theory and the relational history of the thesis as well as the main contents of the dissertation are given in the introduction. After that the main body of the dissertation starts.At first, we construct continuous-time compound binomial risk model. Continuous-time compound binomial risk model is a continuous-time version of the compound binomial risk model in discrete time, its skeleton chain is coincided with the compound binomial model and its limiting case is compound Poisson model. As we know, it is the first model that consider the discrete inter-occurance time random...