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.

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 ρ = 0.047) and accuracy (RMSE ≈ 0.012 $\approx 0.012$ ; MAE ≈ 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.