The Study Between G-expectation And Risk Measures Based On The Representation Of Penalty Function

As the global economy developed rapidly, the financial markets has in constant development and innovation. More and more financial products have appeared which makes financial markets fluctuate greatly and risk measure with product has been increasing. Risk measure as the core of risk management is the guarantee to make the financial markets developed steadily. As China’s financial market not perfectly developed, how to effectively alleviate the risk measures and have a good mechanism in facing the downside risk becomes the focus of the current financial reform. In this paper, we will systematically study the current theories and applications of risk measures in the context of penalty function and acceptance sets.Firstly, we will introduce the definitions and propositions of the risk mea-sure in the sense of acceptance sets, then we will introduce the definitions and representation of convex risk measure, coherent risk measure, law invari-ant risk measure, entropy risk measure and spectral risk measure, the most important thing is to show propositions of risk measures mentioned above, and get links and relationships of them. Secondly, we will introduce the risk measure discussed above in dynamic setting and also give the definitions and properties. Thirdly, we will introduce a new risk measure which is deduced by g-expectation, we have also obtained the sufficient condition of the law in-variance of g-expectations in term of g-probability. Finally, we will give an example of the applications of risk measure in portfolio investment, we will give objective estimations about mean-entropy, mean-spectral models, and get the optimal portfolio which can help investors invest rationally.