The Life Insurance Premium Actuarial Model Under Random Process

Insurance is an important part of modern financial system, with the rapid development of economy, the insurance industry is in rapid development, people’s insurance consciousness is gradually enhanced.Life insurance is an important part of the insurance industry, it is closely related to the interests of the people, it is paid close extensive attention.Premiums is mainly determined by the interest rate, pure premium rate, force of mortality, and the interest rate influence premium most. In recent years,more and more scholars study of life insurance actuarial model under stochastic interest rate. However, almost all scholars regard customers who buy insurance as a fixed group,without considering the randomness of the clients. This paper not only considers the randomness of the clients, but also considers two kinds of randomness of the interest rates.First of all, discusses the background and research significance of the paper,summarizes the research status both at home and abroad, and summarizes the research content and the overall framework of the paper.Secondly, this paper introduces the definition and theorem of counting process,Poisson process, compound Poisson process, a standard wiener process, Liu process, and the nature of digital characteristics. This paper also introduces the principle of payment balance, interest force, present value, pure premium rates, payment methods of life insurance, expressions of five kinds of common force of mortality and density function of death time, provides preparation and theoretical support for the model.Again, regard the insurance process as a Poisson process, divide the clients into three independent parts, and model interest force with standard Wiener process. Consider the income from premium that clients pay and the outcome from surrender charge fee and claims. According to the principle of payment balance, Net single premium model and net annual premium model is built under different force of mortality. After the analysis of the premium model, find that the parameter of the Poisson process has nothing to do with pure net premium. But net annual premium is concerned with the parameter of the Poisson process.Finally, model interest force with fuzzy process and build net single premium model and net annual premium model under different force of mortality.