Law-Invariant Convex Risk Measures And Their Representation Theorems

Financial risk management is one of the most important theories of modernfinances and economics, while measuring financial risk measure is the fundamen-tal work. First, some basic concepts, such as risk,risk measure and coherence, areintroduced. Then as an improvement of coherent measures, we present the convexmeasure and observe its characterization. At last, we do some deeper research in riskmeasures and using law invariance and lower semi-continuity, we provide characteri-zation of the larger class of law invariant convex risk measure and the representationof it.