Abstract:

The linkage of assets has strong network characteristics， and the contagion and spread of risks has gradually evolved from a simple one-way driving relationship to a network-like cyclical interaction relationship. Incorporating the contagion and spillover of risks into the framework of optimal allocation of investment portfolios， and studying the effects of asset volatility clustering and network spreading effects of risks， can provide a new perspective and thinking for avoiding investment risks and comprehensive risk management.Sparse low-rank algorithms and graph network structure-based entropy uncertainty risk models are used to dig deeper into asset characteristics and capture the dependencies between them. Then， using the dynamic tracking strategy of kernel-norm multi-objective matrix regression and adaptive weight learning method to optimize the allocation of portfolios in uncertain environments， the portfolios under nonlinear risk superposition and sparse low-rank optimization Strategy are obtained. It is found that the uncertainty risk model based on network structure entropy can effectively capture the non-linear superposition effect between assets， and the sparse， low-rank optimized portfolio can effectively select high-dimensional assets， and better focus on the allocation of high-quality assets. The income balance is more reasonable， the portfolio performance is more advantageous， and the robustness is stronger. The empirical conclusions have important guiding significance for comprehensive risk management， quantitative portfolio analysis， index fund investment， and risk asset pricing.

Key words: high-dimensional sparse network, comprehensive risk management, low-rank matrix regression, non-negative matrix factorization, link prediction