Adaptive Lasso-CVaR Model With Network Structure And Its Application

With the prosperity and development of China's financial market,the demand for wealth management has gradually diversified,and the number of investment products has increased sharply.The income sequence of some financial products have obvious ‘peak fat tail' distribution,which increases the risk of investment and wealth management.So it is an important concept of portfolio investment to choose reasonable assets to diversify investment risks and gain ideal returns.CVaR is an important risk measure for measuring portfolio investment.It is of great significance to select robust asset portfolio in a CVaR based model so as to reduce both the time cost on management and economic expenditure.In existing research,we found that in the financial market,there is usually a correlation between assets.This kind of correlation undoubtedly brings obstacles to decision-making for investors.Therefore,based on the high-dimensional asset selection problem and considering the asset correlation,an adaptive Lasso-CVaR model with a network structure is developed to select high-dimensional assets in order to achieve the dispersion tail risk and solve the impact of the extreme investment position on investment decision-making in portfolio.In this paper,adaptive Lasso penalty is used to realize asset selection,and the investment weight of assets is estimated simultaneously.This method can select assets continuously and has good robustness.In order to consider the correlation of assets,this paper constructs the network structure of assets based on complex networks,and further uses Laplacian punishment to constrain its relevance.In computational aspect,the adaptive Lasso-CVaR model is transformed into penalty quantile regression,and the model is solved by linear programming.Furthermore,we theoretically prove that the parameter estimation satisfies Oracle property and considers the Monte Carlo simulation of the proposed model under different conditions of n(27)p and n(29)p.The simulation analysis shows that under different quantile points,variables and the distribution of error terms,the new model has the best effect on both variable selection and prediction performance compared with the model without network structure.And the advantage of network structure becomes more and more obvious with an increasing correlation between variables,which shows that network structure indeed improves the function of the model.Finally,249 stocks in the CSI 300 Index are selected and considers f n(27)p and n(29)p for empirical analysis.With a rolling regression technique,under different window width conditions,the model with network structure can well disperse tail risk and the proposed model presents great robustness.In conclusion,the adaptive Lasso-CVaR model proposed in this paper has good theoretical properties and has good application significance.