Abstract: This paper starts from the equity and creditor's rights of the enterprise. An undirected graph network is constructed based on the default distance, and the risk of contagion, spillover, and spread in the form of a network with uncertainty risk is analyzed. The sparse network optimization method using the minimum spanning tree minimizes Non-linear risk of portfolio.From the perspective of resource allocation, sparse clustering algorithms are used to dig deeper into the characteristics of assets and their dependencies are captured, and a multi-objective, multi-index robust matrix regression strategy is adopted to dynamically track market trends.Then, the adaptive weight learning strategy is used to select and configure the asset portfolio under the influence of the network risk overlay.Finally, the sparse clustering optimization strategy of the portfolio under the minimum spanning tree risk is obtained, which further expands the asset pricing multi-factor model. It is found that the sparse clustering portfolio with multi-objective matrix regression not only selectively discards the investment targets in the portfolio, enables funds to be allocated to high-quality assets in a centralized manner, but also helps to reduce or even cut off the spread of risk through the minimum spanning tree.The risk analysis method of financial networks not only effectively describes the non-linear superposition effect of risks infecting each other, affecting each other, and strengthening each other in a network manner.In addition, the compression of asset weights and the optimization of the minimum spanning tree minimize the impact of risk contagion in the worst case.It is a useful supplement to asset allocation and comprehensive risk management in a complex network environment, and provides a desirable investment strategy and decision basis for long-term investment funds to obtain a more balanced asset allocation of risks and returns.This paper follows the research ideas of capital asset pricing, inherits and extends the classic asset pricing model, adds non-linear superimposed network risk to the portfolio optimization model,provides a new perspective for the implementation of comprehensive risk management, portfolio allocation and asset pricing, enriches the understanding of market microstructure and resource allocation efficiency, deepens the understanding of behavioral finance such as market anomalies, and expands the portfolio model and multi-factor Asset pricing model.

Key words: network risk, default distance, matrix regression, minimum spanning tree, sparse clustering, nonlinear superposition