Study on Cumulative Residual Entropy and Variance as Risk Measure

In this paper, we will use a novel measure of information called Cumulative Residual Entropy (CRE) to develop a new measurement of risk and compare it with variance, then conclude the existence of variance is sufficient condition for existence of CRE and there exists a positive linear correlation between CRE and standard-deviation in experiment study. We apply it to solve risk measure problem for some special heavy-tail distribution of non-existence variance.