Bankrupt Theory Of Insurance Risk Model Results

In insurance mathematics, Ruin theory is the mainly contents of insurance risk theory, as can supply a very useful early-warning measure for the risk of the insurance company, it has important theoretical and practical significance for the insurance company. In this dissertation, we get some generalized risk model by extends the risk model in some different aspects. And some results about the ruin probability and present value of dividend payments are discussed. It mainly constants the following results:1. Considering a risk model with time-correlated claims, in which every claim can produce a delayed by-claim randomly according to the amount of it. By means of the Laplace transform and the roots of function, the ruin probability of the risk model is obtained when the claim size is light-tailed. The upper and lower limit bounds of the ruin probability are also studied when the claim size is heavy-tailed.2. A double-type-insurance Cox risk model perturbed by diffusion in a Markovian environment is considered, the exponential upper bound for the ruin probability and the expression of the ruin probability under a special condition are obtained by the Markov vector process martingale approach.3. A generalized Andersen risk model is studied under the condition that the premium arrival process is a finite stream of random events with independent increments, and the claims arrival process is a general renewal process. By martingale method its ruin probability and Lundberg's inequality are obtained. The survival probability in finite time period, the mean and variance of the finite time to ruin in case of exponential claims amount are also studied.4. We also study the generalized Erlang(n) risk model perturbed by diffusion, mainly studied the function of the expected discounted penalty function, especially on some results on the distribution of dividend payments until ruin under risk model with a constant dividend barrier. An integro-differential equation for the moment-generating function of the discounted sum of dividend payments until ruin is derived.Moreover, An integro-differential equation for arbitrary moments of the present value of dividend payments is also derived, and solved the equation when the individual claims amounts have a distribution with rational Laplace transform.