Neural Network Calculation For Robust Expected Shortfall

With the development of financial globalization and new technologies including the Internet,domestic financial markets have become more developed than ever.While the more active markets lead to not only the richer financial instruments but more complex risks,which makes it important to manage it effectively and efficiently.Risk management is the process that contains accurate risk measurements and corresponding strategies which is based on the measurement results.The process of risk measurement can be divided into aggregation of risks and different measures,of which risk aggregation can be understood from the perspective of a portfolio to calculate the total risk,or from the perspective of corporate operations,which is to calculate the sum of multiple risks faced by a company.Mathematically,it is the expected size of the sum of multiple random variables.This paper starts from the perspective of the extreme value of risk aggregation.In order to measure more accurately,we find the extreme value of risk aggregation under some assumptions.The first is to know the marginal distribution of each risk,which is a random variable in mathematics.This assumption not only simplifies our problem but also is practical,because in the actual risk measurement process,the distribution of a single risk is relatively well-measured.At the same time,in order to use more known information about risk and improve the measurement accuracy of the extreme value of risk measurement,we introduce the concept of robustness.The specific method is to first use the historical data and known information of risks to assume a joint distribution of multiple risks.This joint distribution has a good reference significance for the measurement of risks,so it can also be called a reference distribution.Then use the Wasserstein distance to build a fuzzy set about the reference distribution.Finally,take the elements whose edge distribution is consistent with the known edge distribution in the fuzzy set to form a set,and find the extreme value of the risk combination in this set.In terms of risk measurement tools,this paper does not use relatively traditional value at risk,but instead chooses the expected loss with better nature.And the expected loss is more suitable for the neural network method used in this paper.We also introduce the advantages and calculation methods of the expected loss in detail.In terms of risk measurement tools,this paper does not use the relatively traditional value at risk,but chooses expected shortfall with better properties.And the expected shortfall is more suitable for the neural network method used in this paper.We also detail the advantages and calculation of the Expected Shortfall in the paper.In order to use the neural network to calculate the extreme value of the expected shortfall,we first use the duality results of the risk combination problem that have been proved by relevant scholars.The introduction of the duality representation gives us the basis for numerical solutions,and then we construct an appropriate penalty term,The way of adding a penalty term to the duality results enables the original problem to be solved using a neural network without errors due to the introduction of the penalty term.At the end,we use examples to empirically study the above methods.The empirical research results show that the neural network method has high accuracy and wide applicability in estimating expected shortfall.