The Probability Of Bankruptcy Of The Three Kinds Of Reinsurance Risk Model As Well As Bankruptcy Deficit

Risk theory is an important branch of the modern mathematics, which is mainly applied in finance, insurance, risk investment and risk management. Typical Risk Model is the one, in which a stochastic spot process is used to describe the times of claim damages, and a group of separate stochastic variables are used to describe the amount of claim damages. Then by developing and populating it, we get Renewal Risk Model, Cox Risk Model, and etc, thus, risk theory has been pretty mature. This article puts more emphasis on the research on the ruin probability and deficit distribution of several Reinsurance Risk Models based on the elaboration of the development of the risk theory and the senior's results.In the first chapter, we mainly introduced the history of the development of reinsurance.In Chapter Two, we focused on some related basic knowledge, including the result of Typical Risk Model, homogeneous Poisson process, and knowledge related to measures crossing theory and reinsurance.In Chapter Three, Four, and Five, we concentrate on quota share reinsurance Risk Model, Surplus Reinsurance Risk Model and Excess of Loss Reinsurance Risk Model respectively, which mainly included the zero-interest rate one and the one with interest rate, and we got the corresponding manifestation of the ruin probability and the deficit distribution or the satisfying integral and differential equations.This article starts with Typical Risk Model, but it develops according to the concrete situation as not to be confined to the frame of this model and attached tightly to the reality. The models and the results discussed in this article are certainly of some guiding significance to some relatedindustries.