Research on Loss Risk under Incomplete Information

One of the concepts used to measure risk and uncertainty is the variance or the standard-deviation in finance and insurance market. The simplicity of variance and standard-deviation remain a major attraction. But they have some limitations. In this paper, we present a new risk measure which combines entropy and variance under the incomplete information. The estimate of maximum entropy loss distribution and the value of entropy function are obtained by the maximum entropy principle which is very important in information theory. The resulting distribution is least committal with respect to unknown or missing information and is, hence, the least prejudiced. The entropy and variance of the distribution are used to measure probability risk and the disparity of the loss from the mean. This new method is more comprehensive forecast to loss risk because entropy is relative to more moment information. Further, we show an example to illustrate and demonstrate the maximum entropy and variance under various moment constraints.