On The Negative Risk Models

The insurance industry as one of the "three carriages" of the modern financial industry has an important function of modern economic and social escort. Financial and insurance industries are at the heart of the modern economy and effective supervision and management of financial and insurance industries has a great significance for the healthy and stable operation of the entire national economy. Risk management and control of a company has a very important impact on the company’s operating.According to the different claims, the risk models can be divided into positive risk model and negative risk model. With the development of insurance and risk theory, negative risk model has aroused keen interest of many scholars in recent years. Domestic researchers of the negative risk model are more and more, such as Liu Zaiming, Wang Yunjie, Xiong Shuang and so on.As the development of the insurance industry, the dividend insurance products are more and more. Finding the optimal dividend strategy has become a hot topic in the study of risk theory. In addition, scholars pay attention to the capital injection and reinsurance strategies reducing the ruin probability and some foreign scholars have more in-depth study of the negative risk model under these cases, such as in [8-9]. To study the optimal control strategy of these risk models, it often uses the stochastic control theory.Now the research on the negative risk model is not a lot, and most of the studies of negative risk model are under the case of Poisson process. This thesis will study the negative risk models with compound binomial process, compound negative binomial process or the optimal dividend and capital injection strategy.This thesis first introduces the research background of the negative risk model and the relevant conclusions of the negative risk model. Considering the different claim ways, we define a negative risk model which contains two types of insurance and get the ruin probability. Considering dividends and allows the injection capital, we define a negative risk model and derive the optimal dividend strategy in different situations.This paper mainly constants the following results:In Chapter2, Considering the negative risk model under compound binomial process or the compound negative binomial process, we get the ruin probability.In Chapter3, the negative risk model allows the injection of capital, and we get the corresponding HJB equation to explore the optimal dividend and capital injection strategy.