On The Consistency Of Credibility Premium Under The Balance Loss Function

Since the 21st century, the insurance industry in China, especially non-life insurance business has developed very fast and the company scale expands rapidly. For an insurance company, premium income is not only the most important channel of capital inflows, but also the main sources of funding to fulfill responsibility. The premium is the main impetus of asset growth, also leads to the increasing in insurance liabilities. It is far from completion for domestic insurance industry, such as premium rate is uniform in China instead of different insurance companies have different premium rate. However, with the continuous development and the persistent improvement of the insurance market, the system on the premium rate in China will be changed.The process of determining Premium rate is critical to the setting of premium while the reasonableness of the premium will relate to stable operation and sustainable development of insurance companies directly. There are many ways to estimate the premium rates, such as pure premium method, the index theory, the Bayes premium, Esscher's premium method, credibility premium method and so on. In the traditional credibility theory, symmetric loss function being used frequently to measure the risk variables. Later many scholars found that in some cases it is more accurate and reasonable by using asymmetric loss function to measure the risk. We usually make use of consistency to test the reasonableness of the estimated premium. Intuitively speaking, the estimated premiums possess consistency, if it infinitely closes to the individual premiums under certain conditions. Consistency is a fundamental requirement for the estimated premium. We say the estimated premium is reasonable and accurate when it meets the consistency. Asymmetric loss functions include the balanced loss function, the entropy loss function, etc. In this paper, we describe the derivation of Esscher's credibility premium theory and the consistency of this theory on the base of the balanced loss function and a new function ( )H nX related to empirical data. We show that this theory meet the requirements of consistency under certain conditions. It is worth noting in this paper that instead of using the mean of empirical data, we introduce the function ( )H nX defined in the Mao-lin Pan(2007).This paper includes three parts. In the first part, we introduce the principles and methods of setting premium. The principles include sufficiency principle, fair and reasonable principle, stable and flexible principle and loss prevention principle. The methods include increasing and decreasing, observation and classification. In the second part, we focus on a number of classic premium principles, including the pure premium principle, the index theory, Esscher theory and credibility premium theory, as well as the form of credibility premium under the principle of Esscher. What is more, we introduce the balance Loss function and derive the specific form of Esscher's credibility premiums with this type of balanced loss function. In the third section, we discuss the consistency of Esscher's credibility premium and prove that Esscher's credibility premium posses consistency under certain conditions.In summation, we analyze a method of determining premium rates, aim to find a more reasonable premium in some situations. This method is a supplement of determining premium rates theory.