This article proposes a new coherent risk measure called iso-entropic risk measure, which is based on relative entropy under the theory framework of Artzner et al.(1999). It is pointed that this measure is just the negative expectation of the risk portfolio position under the probability measure through Esscher transformation. This iso-entropic risk measure is not a 0-1 risk measure and very smooth in contrast with another important coherent risk measure AV @R (Average Value at Risk). And it is a little larger than AV @R at the same level, name...
