Abstract: The axiomatic system of coherent risk measures has set up by Artzner et.al. owever, the mathematics underlying it is closely related to the ideas of convex otimization, specifically the duality theory. This paper simply proved the general  expression of coherent risk measures by the cone duality theorem in finite dimension space.  We have analyzed the core role of acceptable set in coherent risk measure and the properties  of conventional risk measures. In spite of the size of acceptable set may be used for controlling the risk management strictly or loosely, but we do not know how to express it quantitatively.   The paper suggest  In addition we suggest relaxing no arbitrage condition in view of the flexibility of coherent  risk measures and the achieved results may be used to pricing option in incomplete market.