The Ruin Probability Of Time Relevant Risk Model

Risk theory is a very important part in actuarial, which make use of the methods of probability and stochastic process to establish mathematical about insurance company's management, and model according to analysis. On the theory of collective risk model, Ruin theory studies the probability of insurance company' surplus becomes negative for the first time after a period of running of the insurance company with certain initial reserve.In this thesis, an introduction to the development and present situation of life insurance is given at first, and then the mathematic models of general life insurance are described. The methods and the main conclusion is also introduced.In Chapter 3, by taking a further investigation into the Double Poisson Risk Model, that the happening of premium and claims are regarded as two independent Poisson process respectively, we establish a derivational model which the happen of premium and claim are relevant in time. Then by transforming the model, we get the equality and inequality of the ruin probability.In Chapter 4, we add interference to the derivational model. Also by studying the transformed model, the inequality and the upper bound of the ruin probability both by final time and infinite time are obtained.