A Study On Life Insurance Reserves Under The Environment Of Stochastic Interest Rates And Mortality

A Study on Life insurance Reserves under the Environment of Stochastic Interest Rates and MortalityThe insurance in China is an emerging industry, three decades of reform and opening up have witnessed the rapid development of this industry. However, the rapid growth doesn't only rely on market demand, but also more dependent on actuarial theory. For example, the calculation of premiums, reserves for extracting and so on. From start to finish, how to extract reserves has been a great concern for insurance company, and it is a key to the healthy development of insurance companies. If reserves are fewer, problems will appear in the solvency of insurance companies,and they could face bankruptcy risk. If reserves are more, they can not meet the investment needs of insurance companies. Accordingly, calculation of reserves has been the focus of attention at home and abroad, and how to extract the correct amount of reserves in a complex market environment is a key point in actuarial science.After a policy was issued, the insurance company will be responsible to the insured or the group, If the insured died during the period of insurance, or other conditions happens, the insurance company must fulfill corresponding obligations. Before the occurrence of the risk, insurance companies need to build up some assets to address these to the responsibility, the majority of these assets are from the premiums. In a word, the reserves is to ensure that insurance companies will meet the responsibility for the future. Today, with the development of China's insurance industry China Insurance Regulatory Commission has strengthened its supervision, especially in the supervision of the reserve, It is prohibited that insurance company the adjust reserve to meet the profits and solvency status.Under normal circumstances, the calculation of life insurance reserves (hereinafter referred to as reserve funds) generally make use of fixed interest rates and determined mortality rate, but in real life, which, interest rates and mortality are random, especially in the past few years, when the world financial crisis broke out, as well as the fluctuating market prices,adjustment of interest rate is the necessary measures in the national macro-control. And in the current prevalence of human variety-borne diseases (such as H1N1), human life table is no longer static, and human mortality also show some kind of random fluctuation phenomenon. This paper concentrated on discussing the computational methods of life insurance reserves under the circumstance of stochastic mortality and interest rates.What's more, I have calculated reserves of a group of policy by making use of regression equation which based on the stochastic interest rates.The full text of a total of five chapters, three parts:The first part is the introductory part of the first chapter, which describes some of the major topics of the background and significance of the status of research at home and abroad, as well as point and lack of innovation in this paper. This part generally introduces the importance of the reserves so that we have a preliminary understanding.The second part is Chapter two and three. The second chapter provides some theoretical approaches to the process of computational methods in details. First of all, interest theory is a basis for actuarial science, it is mainly around the time value of money. Secondly, in actuarial survival model, life table plays an important role.It is one of the main basis for pricing. Life table is not a simple statistical data, it is based on census during a period of time within a country or a region, and then to collate. Again, life insurance actuarial mathematics provides a theoretical basis for the calculation of variety of data, For example,when we have calculated the net premiums, we mainly make use of the principle of equivalence, that is, premiums paid by the insured person should be equivalent to his risk. And then on the transition to the gross premium which is attached to the profits and costs of insurance companies. The insured should pay the gross premium at the end. There also has introduced the definition of reserves and the general calculation method to calculate the reserve which can be divided into two ways:the past and the future. The third chapter models stochastic mortality and interest rates, indicating mortality and interest rates are random in some cases. We chose the AR (1) of this model because we can easily calculate the first and second moments of the discount function and covariance. Secondly, we have also done detailed definition for stochastic mortality.The third part is the chapter four and chapter five, and it is the core part. Chapter four makes the use of the model of Chapter three, and has discussed on the computational methods of life insurance reserves under the circumstance of stochastic mortality and interest rates. Firstly, we define the prospective loss random variable for the whole portfolio, and then we obtain the reserves by calculating the expected value of this random variable. In addition, we are defined prospective loss random variable L under the stochastic interest rate and stochastic mortality, and the prospective loss random variable M under the stochastic interest rate and determined mortality. When the number of policies is large, we can approximate the prospective loss random variable L by M. At last, we set an example in chapter 5 to calculate reserves of a group of policy, and compare the case that does not consider years and costs.