From an investor's view,risk is closely related to his investment target.In this paper we take the investment target into the risk definition,and propose a new axiomatic framework for the class of generalized coherent risk measures.It proves that the class of generalized risk measure is consistent with the individual's risk preference.The put option premium is an intuitive risk measure,and also is a generalized coherent risk measure.Connections between the put option premium and other risk measu...