Application Of Singular System In The Insurance Company’s Surplus Problem

This paper mainly studies the application of singular system in the insurance company’s surplus problem. The main conclusions in this paper are:(1) The development process of singular system and the application in the economy of singular system are introduced respectively. In addition, recent research achievements of the insurance company’s surplus problem are introduced.(2) This paper considers about the relationship of insurance company among accumulated surplus, investment return, the premium and claims, as well as the relationship between the premium and claims, daily consumption, and considers the interaction between different types of insurance, then the paper uses system thought to set up accumulated surplus expression of insurance companies. After analyzing the system, the paper presents the expression and numerical examples in the corresponding system.(3) The paper discusses the problems of the surplus system’s stability in insurance companies. Because of the stability studies under normal system model is difficult, so the paper considers the stability of two special cases. When there is no interaction between different types of insurance, system is not stable, and the risk of company management is bigger. If transition probability from different insurance products to the same insurance product is same, the system is also unstable. The paper also considers about the stability of the singular system, the result turn out that the system is stable. Then the paper gives numerical examples respectively based on three different situations, and draws the pole program for validation.(4) The change of parameters, such as return on investment analysis, has an impact on accumulated surplus. Due to changes in parameters can bring more profits, but it may cause the system to become unstable, So in view of accumulated surplus unstable system in insurance companies, the paper finds the stabilization of the model by state feedback. Finally the paper considers the practical value of the model, causal analysis of the model and present that the model under normal system is clearly causal, then the paper considers the model under the singular system, and proves that it is causal by using the mathematical induction.