The Research Of Quasi-convex Risk Measure And Price Bubble Problems Based On Banach Spaces Model

The measurement of risk in financial markets had become the core of the industry investors and the relevant regulatory authorities of the economic activity. Theories and methods of measurement of financial risks had a lot, such as VaR, CVaR, coherent risk measure, convex risk measure, quasi-convex risk measurement and so on. After decades of theoretical innovation, risk measure theory had achieved outstanding research results and theoretical framework. Because of the strict conditions of coherent risk measure, and a certain gap between the actual economic environment, so the quasi-convex risk measure had an advantage in the characterization of risk diversification and liquidity projections.And it’s welcomed by scholars in recent years.At the same time,the researches and applications of the theory made a series of research results.In recent years, Kountzakis (2013) proposed the coherent risk measure based on the Banach spaces theorems, and combined with Price-Bubbles, achieved some meaningful results.This paper is based on the studies of Koutsakis ideas, and studied the quasi-convex risk measure of Banach spaces.Then gave the results of the corresponding representation theorem.First of all, we gave the representation theorem of quasi-convex risk measure in Banach spaces, and studied their related properties.Then gave the equivalence relation between the two quasi-convex risk measures.Secondly, we defined the quasi-convex risk measure about unsure spaces,then gave the criterion of unsure spaces and the corresponding examples.Finally, we combined the unsure subspaces and price-bubbles theory, and gave a specific example.The results obtained in this paper could be regarded as a natural generalization of works by Kountzakis.