Research On Claims Risk Based On Policies Information

Claims risk is not only the theme of insurance risk theories, but also one crucial risk faced by insurance companies in reality. Throughout the existing literatures, ruin probability is always the core issue of theoretical research on claim risk, which is based on the framework of Classic Risk Model (Cramer-Lundberg Model). From a practical perspective, Classic Risk Model with the hypothesis of linear income and a package of claims doesn’t take the relation of premium incomes and claims as well as policies information into consideration, which leads to an inaccurate description for informationization and complication of insurance business. All of these defectives are made up by a new risk model, named Modern Risk Model, which is built by Li et. al. and is more in line with the operational characteristics and management requirements of modern insurance business than the classicBased on the background and framed by Modern Risk Model, this article is devoted to the ruin probability as well as risk measure of non-life insurance with full consideration of policies information. After some literature reviews on risk theory, ruin probability and financial risk measure, and along with the research paradigm of classical risk model, this article consists of three main contents:firstly, based on micro policies information, we obtain the upper bound estimate of ruin probability in the case of small claims by the methods of stochastic process and embedding technology (the main content in Chapter 3); secondly, on the same basis of micro policies information, and by the use of heavy-tailed distribution as well as limit theory, we achieve asymptotical equivalent estimate of ruin probability in the case of large claims (the main content in Chapter 4); At last, we construct some new risk measures based on macro policies information, and conclude the equivalence of local measure and the whole history measure by taking advantages of Poisson process and the properties of the regular tail distribution, which is just satisfied with the condition of large claims (the main content in Chapter 5).Among these studies, the first two can solve the problems for estimation of ruin probability no matter in the case of small claims or large claims theoretically. At the same time, they can provide the theoretical basis for the design, pricing, risk evaluation and the scoping of the initial capital of non-life insurance. And then, the conclusion of the third study, which focuses on one more realistic background of risk control for the large claims, shows the local measure can be used to instead of the whole history measure if we can have an appropriate measure method. Also, this conclusion can be confirmed to own the realistic value, which not only lies in cutting down the costs of time and information in the process of risk evaluation effectively, but also can provide a unique perspective and a clear path for risk control. Moreover, all of these results can be displayed intuitively and caught an effective auxiliary validation by the MATLAB programming and numerical simulation.