External shocks such as oil-price movements, exchange-rate shifts, and global risk sentiment can affect not only aggregate equity performance but also how stress propagates across sectors. This paper aims to (i) map how these global shocks enter the Chinese equity market, (ii) identify which sectors amplify or buffer their transmission, and (iii) provide an interpretable framework that can support stress testing and portfolio risk monitoring. We adopt a complex-systems, network-based perspective and use information-theoretic dependence (mutual information) to learn time-varying inter-sector linkages. Global financial markets are increasingly interconnected, and external shocks transmit unevenly across sectors. We study how oil, currency, and volatility shocks propagate across Chinese equities using a novel Graph-VARX that combines vector autoregressions with network methods to capture both direct responses and inter-sector dependencies. The dataset merges daily sector returns with Brent/WTI prices, USD/CNY, and Volatility Index (VIX). Out-of-sample checks confirm stability (spectral radius rho = 0.047) and accuracy (RMSE approximate to 0.012 $\approx 0.012$ ; MAE approximate to 0.009 $\approx 0.009$ ). Results show asymmetric transmission, with the exchange rate the dominant spillover channel. Scenario analysis suggests a +1.5 % RMB appreciation coincides with modest benchmark declines centered in Property and Information Technology, while a +15 % oil increase lifts Materials and Energy and only mildly supports the benchmark. Mutual-information filtering retains 39 of 156 sector links; Utilities, Consumer Staples, and Healthcare act as buffers. Currency dynamics, more than commodity cycles, shape systemic vulnerability and portfolio risks. Further studies extend Graph-VARX to firm-level panels and compare with other emerging markets to test whether hub-periphery patterns are China-specific.

This study examines the dynamic range of financial networks in the Chinese stock market between 2019 and 2021. It provides an objective assessment of the network’s characteristics and scalability. The research time-frame is divided into three segments, reflecting the fluctuations of the financial market, including stable, volatile, and follow-up periods. To establish correlations among companies, the study employs the partial mutual information distance (PMID) method, followed by the construction of three minimum spanning tree (MST) networks for each period. Given the non-linear nature of financial phenomena, PMID is found to be more appropriate than linear methods in the study of financial markets. Additionally, the power law is observed in all three networks. This study is organized hierarchically into levels of nodes, clusters, and global indicators, providing a comprehensive perspective on network behavior and adaptation. Three-level indicators are calculated for each of the three networks, and the findings display a noteworthy variation between the volatile network and the other two networks. During stable and follow-up periods, a node-level analysis has indicated strong interconnectedness among companies. In contrast, during volatility, there are dynamic fluctuations in network dynamics. Cluster-level analysis reveals that firms become more essential connectors and actively engaged, with increased centrality. A global analysis shows that companies are more likely to form partnerships with counterparts possessing similar degrees during times of market volatility compared to periods of stability or follow-up periods. To assess the resilience of the constructed networks, we employed Markov chain analysis and examined the maximal connected component (MCC); the study findings suggest that the network is more susceptible to volatility in the observed second period, while demonstrating greater resilience in the follow-up period indicating recovery of financial markets.

Portfolio management has long been one of the most significant challenges in large- and small-scale investments alike. The primary objective of portfolio management is to make investments with the most favorable rate of return and the lowest amount of risk. On the other hand, time series prediction has garnered significant attention in recent years for predicting the trend of stock prices in the future. The combination of these two approaches, i.e., predicting the future stock price and adopting portfolio management methods in the forecasted time series, has turned out to be a novel research line in the past few years. That is, to have a better understanding of the future, various researchers have attempted to predict the future behavior of stocks and subsequently implement portfolio management techniques on them. However, due to the uncertainty in predicting the future, the reliability of these methodologies is in question, and it is unclear to what extent their results can be relied upon. Therefore, probabilistic approaches have also entered the research arena, and attempts have been made to incorporate uncertainty into future forecasting and portfolio management. This issue has led to the development of probabilistic portfolio management for future data. This review paper begins with a discussion of various time-series prediction methods for stock market data. Next, a classification and evaluation of portfolio management approaches are provided. Afterwards, the Monte Carlo sampling method is discussed as the most prevalent technique for probabilistic analysis of stock market data. The probabilistic portfolio management method is applied to future Shanghai Stock Exchange data in the form of a case study to measure the applicability of this method to real-world projects. The results of this research can serve as a benchmark example for the analysis of other stock market data.

The global financial markets are greatly affected by crude oil price movements, indicating the necessity of forecasting their fluctuation and volatility. Crude oil prices, however, are a complex and fundamental macroeconomic variable to estimate due to their nonlinearity, nonstationary, and volatility. The state-of-the-art research in this field demonstrates that conventional methods are incapable of addressing the nonlinear trend of price changes. Additionally, many parameters are involved in this problem, which adds to the complexity of such a prediction. To overcome these obstacles, a Mutual Information-Based Network Autoregressive (MINAR) model is developed to forecast the West Texas Intermediate (WTI) close crude oil price. To this end, open, high, low, and close (OHLC) prices of crude oil are collected from 1 January 2020 to 20 July 2022. Afterwards, the Mutual Information-based distance is utilized to establish the network of OHLC prices. The MINAR model provides a basis to consider the joint effects of the OHLC network interactions, the autoregressive impact, and the independent noise and establishes an intelligent tool to estimate the future fluctuations in a complex, multivariate, and noisy environment. To measure the accuracy and performance of the model, three validation measures, namely, RMSE, MAPE, and UMBRAE, are applied. The results demonstrate that the proposed MINAR model outperforms the benchmark ARIMA model.

In this paper, a probabilistic form of the portfolio selection problem is established in which the uncertainty of risky assets is considered through a probabilistic optimization problem. To this end, by taking seven portfolios of Shanghai stock as a case study, the mean and standard deviation of daily return values are calculated based on five years of real data. The optimal values corresponding to each random case were then stored as a comprehensive database of system responses. Then, by sorting the resulting optimal values from best to worst, the exceedance probabilities of return and risk rankings were calculated for each portfolio and presented in the form of probabilistic pie charts. The results showed that the portfolio with the highest deterministic rate of return has the highest probability of getting the best return ranking as well. However, since the probability of risk in all cases was calculated, the probability of each portfolio to place in the lower rankings (i.e., ranking 2–7) could also be discussed. Additionally, to check the convergence of the model, the probability values calculated by the Monte Carlo method against the sample size were plotted to ensure the accuracy of the final answer. Eventually, by generating Gaussian random noise and importing it into the model input, probability changes were calculated to assess the robustness of the proposed algorithm.