Dynamic Systemic Risk Measure And Dual Representation

Risk measure refers to the use of mathematical axiomatization methods to define a mapping which from a random variable to a real number to provide a risk quantification method for financial products,and based on this,to prevent risks in actual economic activities.The commonly used risk measure include consistent risk measure,convex risk measure,and dynamic risk measure.However,these risk measure generally only consider a single financial product,ignoring the connections between multiple financial products.Therefore,in recent years,many scholars have begun to study multidimensional risk measure,Among them,systemic risk measure is a highly promising research topic in multidimensional risk measure in recent years.This paper considers combining systemic risk measure with dynamic risk measure to study dynamic systemic risk measure.This paper can be mainly divided into two parts: The first part reviews the classic risk measure theory and some commonly used basic knowledge in the theory of risk measure.The classic risk measure theory includes one-dimensional risk measure,onedimensional dynamic risk measure,set-valued risk measure,etc;The second part is the main work of this paper,which defines dynamic systemic risk measure under a general framework,including the definition of conditional systemic risk measure and time consistency.Furthermore,the existing results of classical one-dimensional dynamic risk measure are extended to the dynamic systemic risk measure under the framework defined in this paper.