Research On The Several Risk Models

Risk theory is an important theory of actuarial mathematics. With the development of probability and random process theory, risk theory has also been improved. And this makes national insurance grow rapidly. In addition, more and more scholars begin to research many different risk models using various mathematical theory and methods,and get a lot of novel conclusion. For insurance company, the two most important aspects are:one aspect is called the surplus—the investment of policy-holder, the other is called claim amount—the insurance company will compensate for the policy of holder, when insurance company in agreement with policy-holder and expected risks has happened. So on the research of claims and surplus of risk models will be crucial, when they changes, the conclusion of the corresponding models will be changed. So the business of insurance company and products are depended on the research of risk theory. For the risk models, the ruin probability is an important research objects, that is the probability of the time that first surplus is zero. But in the fact, insurance company is facing bankruptcy when the surplus as a limit below. So the two aspects are discussed. The research of the ruin probability provides early warning.In recent years, interference with brown has become the hotspot. In addition, Considering the inflation rate and investment rate as a random disturbance, the estimate of insurance policy became very complicated. Based on above defects of some aspects of the classical risk model and refer to the risk models of Ambayaspitiya (1998), cossette and Marceau (2000), poisson process was introduced. This paper establishes the risk model of surplus and claim with the interference, and more risk models with vary bankruptcy and the brown interference,the risk model with rate,the two-dimensional risk model. Finally, we get the probability and inequality of these kinds of risk model using and the concept of martingale. These models are the promotion of classical risk model, that provide more risk models of objective reality for the risk management process, which have certain practical value.