The Property Of Cumulated Residual Entropy And Its Application In Investment Risk

This paper mainly studies the nature of accumulated residual entropy and its application in investment risk,and provides theoretical support for venture capital and decision making.The first chapter mainly deals with the development process of accumulated residual entropy and its development significance.The second chapter mainly introduces some classical inequalities and theorems as preliminary knowledge,which lays the foundation for the proof of accumulated residual entropy.The third chapter mainly studies the basic properties of the cumulative residual entropy,and study the relationship between the cumulative residual entropy and variance,compared the cumulative residual entropy and variance of several common distributions,the cumulative residual entropy and variance of the applicable scope,it is concluded that the cumulative residual entropy of a broader scope than the variance.The fourth chapter analyzes several classic risk measurement models and introduces the principle of measuring risk,which emphasizes the accumulation of residual entropy model.The fifth chapter gives examples to verify the advantages of accumulated residual entropy model and the linear relationship between accumulated residual entropy and standard deviation.In sixth chapter,the coding theorem of the non-memory source is extended to the case of non-homogeneous markov chain sliding average,and the simple application of the theorem in the hypothesis testing is given.The seventh chapter briefly analyzes the existing problems of this subject,and gives a preliminary prospect for the development prospect of accumulated residual entropy.