Uncertain Risk Analysis And Uncertain Insurance Analysis

Real decisions usually face risk because of the imprecise information or lack of information. Because the uncertain risk may bring about the potential losses, insurer comes into being in order to recompense the losses. For a long time, it is always one of important issues to study the risk and insurance in uncertain environment.This dissertation employs uncertain variable to describe the uncertain risk and investigates the risk and insurance in the framework of uncertainty theory. Based on uncertain measure, some types of risk measures are first introduced. In order to compare the risks, three kinds of comparison rules are designed and the accord-ing comparison theorems are proved. Based on the uncertain risk measures, the uncertain premium price problem is investigated. With the help of the utility the-ory, the uncertain net premium is proposed. Then, the uncertain expected value premium and uncertain distortion premium are derived from the uncertain net pre-mium. Next, some properties of uncertain distortion premium are discussed and a characterization theorem is proved.As an application, an uncertain optimal reinsurance model is built based on the uncertain value-at-risk measure and expected value premium. Meanwhile, a sufficient and necessary condition that the proposed reinsurance model has optimal solution is provided. Finally, some numerical examples are given to illustrate the model. This dissertation provides a method to study deeply the risk measures and insurance premium in uncertain environment.The highlights of this dissertation includes:1) Defining three types of uncertain risk comparison rules, proving according comparison theorems;2) Proposing the uncertain distortion premium, discussing its properties and proving a characterization theorem;3) Building an uncertain reinsurance model, proving a sufficient and necessary condition that the model has optimal solution.