1.1. Research gaps and motivation

The existing research of capital allocation and portfolio optimization, ongoing advancements through the application of ML, DL and limited DRL approaches. Despite these developments, major research pitfalls on how to effectively address time-varying uncertainty, stability of the learning policy, and risk-sensitive stability of the action selections have not been solved yet. For example, most DRL approaches based on the DQN [27] were facing problems of overestimation bias and unstable value convergence under unpredictable market dynamics, reducing the possibility of reliably stabilizing a stable but increasingly volatile investment portfolio. Similarly, policy-gradient DRL algorithms, such as PPO [29], enhance training stability even further, but continue to have slow adaptation capabilities in response to meaningful regime changes and were sensitive to reward designs.

To overcome these limitations, the proposed DAC-CPPO method facilitates stable policy updating, decreased gradient estimate variance, and convergence-stability. The DRL implementation provides a stable convergence, risk-conscious DRL approach adaptable to dynamic market environments. Consequently, the proposed principle-driven method effectively resolves DRL shortcomings by optimally allocating capital in risky financial markets. The main research contributions of this work are described below,

• Propose a Dynamic Actor-Critic enriched CPPO (DAC-CPPO) model for more adaptive and stable portfolio optimization.
• Obtains risk-aware reward mechanisms that preserve capital in periods of market volatility and uncertainty.
• Provides a means of stabilizing policy updates (using clipping), which diminishes the gradient variance in training and avoids destructive large movements in parameter space.
• Demonstrates superior risk-adjusted performance compared to traditional and standard reinforcement learning portfolio strategies.

2.1. Data collection and source description

Massive Yahoo Finance Dataset (Yahoo Finance Dataset Historical Stock Market Information of Top 500 Companies). The data at https://www.kaggle.com/datasets/iveeaten3223times/massive-yahoo-finance-dataset and Intelligent Finance Dataset (Market indicators and capital allocation signals for adaptive portfolio decision) https://www.kaggle.com/datasets/zara2099/intelligent-finance-assets-dataset, contains 7000 time-indexed financial records. Both datasets are publicly available Kaggle datasets used for financial analysis and portfolio optimization research purposes. Historical stock market data spanning five years were collected from Yahoo Finance for this dataset. It contains daily records of stock performance measures of the best 500 companies, spanning a period of five years by market capitalization, and the Intelligent Finance Dataset contains fielded financial market data that is intended to be used in classifying an asset and also in intelligent portfolio analysis. It incorporates historical price data, trading, behavior of returns, volatility, and financial risk measures to enable advanced financial modelling and predictive analytics. The dataset is split using a chronological (time-series-based) partitioning strategy, where 80% of the earliest records are used for training, and the remaining 20% of the most recent records are used for testing. To avoid look-ahead and data leakage biases, all financial features employed in training the model have been calculated solely based on historical observations up until the point of prediction. Neither future stock prices, nor returns, nor portfolio results, nor market information have been included at any stage of the feature generation or state representation process. The projection matrix obtained through the LDA transformation has been applied only to the testing set after being trained on the training set. The train-test split is done chronologically to ensure proper preservation of the temporal order of market observations. This provides a realistic assessment in financial forecasting application. It shows the financial account documents to file a portfolio based on the records, feature variables and target categories which is as displayed in Table 1.

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Table 1. Key features and target variables of financial datasets used in the research.

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2.2. Financial data cleaning and normalization process

Preprocessing involves cleaning data of missing and noisy values and Z-score normalization to set features to a zero mean and unit variance, precluding instabilities and bias in training and enhancing prediction of financial data.

Data cleaning: Data cleaning was performed to correct inaccuracies, missing values and errors in the financial data set before usage in training of the model. In this research, the missing stock prices and anomalous trades with their appropriate imputation methods. Specifically, missing values were handled using linear interpolation for short gaps and forward-filling for sequential missing trading records to maintain temporal continuity. Outlier detection was performed using the Z-score method, where data points with a Z-score greater than ±3 were considered abnormal and treated as outliers. These outliers were either removed or capped, depending on their severity, to ensure stability in model training.

After cleaning, the data set was normalized with Z-score after data clearing and the normalized data was set as input to the model. The normalized data set provide a more accurate and steadier dataset.

Z-score normalization: This process normalizes all the features using a normalization method called as Z-score normalization to get all features on a comparable scale. This makes the features trading volume, stock returns and technical indicators comparable, as well as improving the stability of the Actor-Critic network by reducing the effects of extreme values. The normalization can be described as follows by using equation (1).

(1)

Where is the raw value of the data set, is the mean value, is the standardized value, and is the standard deviation of the feature.

The output from this preprocessing, including cleaned data and normalized features, is a refined dataset that enhances LDA extraction by improving feature consistency, reducing noise, and ensuring more accurate portfolio optimization. Furthermore, the final processed dataset is structured in chronological order before model training to prevent information leakage in financial time-series forecasting.

2.3. Linear Discriminant Analysis (LDA) based financial feature extraction for portfolio optimization

This process uses the preprocessed data to obtain discriminative features, diminish noise, and make LDA effective in stabilizing the DAC training to maximize portfolio performance. Being a supervised dimensionality reduction method, LDA projects the high-dimensional data into a lower-dimensional space by maximizing the amount of variance between classes and minimizing the amount of variance within a class through the best projections. An intelligent portfolio allocation model uses the LDA to minimize co-relationship among financial indicators in prices, MACD, volatility, volume, and returns. This lowers noise, the risk of overfitting, improves the patterns of discriminative markets, and stabilizes the training of DAC. Consequently, LDA strengthens state representation, supporting stable and risk-aware portfolio optimization.

Equation (2) illustrates the Maximized discriminative financial features, improving DAC learning stability performance. It is used to reduce data dimensions by maximizing class separation and minimizing similarities, improving feature discrimination for portfolio allocation.

(2)

Where is represented as an Optimal projection matrix, is the projection vectors, is the financial data, is the transpose of financial data, reduced dimension size is denoted as , denotes the between-class scatter matrix, denotes the within-class scatter matrix, is mentioned as determinant value, denotes the argument of the maximum function, and is the feature vector. Between-class scatter is mathematically represented in Equation (3), which determines the proportion of total wealth to allocate to each asset, optimizing for expected return and risk.

(3)

Reduces intra-class financial noise, improving risk-adjusted feature consistency significantly. It is mathematically described in equation (4). In Equation 4, the market's current condition and the returns expected from assets guide portfolio decisions based on past and present data.

(4)

is the Number of classes, is the within-class scatter, is the number of classes, is the class mean vector, is the global mean vector, is the mean difference vector, denoted the summation of overall response, is the Transpose operator, and the Class sample set and Individual sample vector are denoted as , is the sample deviation and Eigenvalue importance score.

The projection vectors are obtained by solving the generalized eigenvalue problem. Equation (5) calculates the portfolio's performance (reward) based on returns and risk, such as the Sharpe ratio, balancing profitability and volatility.

(5)

eigenvectors corresponding to the largest eigenvalues eigenvectors corresponding to the largest eigenvalues, is the Optimal basis vector, mathematically presented in equation (6). It produces compact state inputs, accelerating Actor–Critic convergence performance. Adjusts the policy (portfolio weights) based on reward feedback, promoting better decision-making in future actions for optimized returns.

(6)

is the reduced state vector, is the projection matrix transpose, and is an original feature vector. LDA gives concise, inherently discriminative financial feature vectors, removing noise and redundant information. This transformation ensures compact, noise-reduced, and highly discriminative state representations, which are then passed to the DAC-CPPO model to improve convergence stability, accelerate learning, and enhance risk-aware portfolio allocation performance.

2.4. DAC-CPPO for intelligent portfolio optimization

A reinforcement learning framework by combining the use of DAC and CPPO in portfolio investment was designed for intelligent capital allocation. The Actor Critic mechanism allowed for flexible policy learning and value estimation in the dynamic non-stationary market. CPPO helped to provide stable convergence of policy learning and prevent over-rebalancing and reallocation of the portfolio by clipping at an ideal probability ratio. This framework achieved significant improvement in convergence stability, Sharpe ratio, long-term risk adjusted capital allocation and avoided over-rebalancing of the portfolio that causes severe drawdown risks.

2.4.1. DAC model for multiple agents interacting with market scenarios to update shared network.

DAC is deep RL algorithm, compose two neural nets. One is Actor Network, which learns a policy , the action that enhances the choice (invest every county to certain proportion of total capital) according to the state of market body. Another is Critic Network, which evaluates the action taken by approximating the value function , function value to giving the actor a useful guidance to make a better decision. The main feature of DAC is that it is an asynchronous parallel training, which means that the agents can adapt to various market conditions at the same time and modify one global network of policies. It also results in more reliable stability as well as a faster rate convergence. It can be applied to make flexible financial decisions, generate continuous policy, give a considerable attention to the detailed capital allocation, and practical-flexible adaptation the ability of market environment under the support from DAC.

The state space represents market conditions, including stock prices, trading volume, and volatility indicators. The action space defines portfolio allocation weights, while the reward measures risk-adjusted returns, optimizing performance through return–volatility trade-offs.

Processes normalized market states, such as prices, MACD, volatility, and portfolio weights, are in Processes in the DAC Input Layer to learn smoothly on. Hidden layers are the further developed layers that extract time and latent market characteristics and highlight the significant indicators in the predictive allocation. To obtain risk-sensitive portfolio weighting based on a activator, Actor Network is applied, which optimizes a sum-to-one allocation that is stable. Critic Network: Reckon expected returns with TD error and benefit functions to evaluate values. Output Layer generates an allocation output of CPPO to stabilize an allocation output, to avoid extreme updates used to achieve adaptive, risk-aware, and high Sharpe ratio performance in dynamic financial markets.

Prevents large policy updates by clipping probability ratios, ensuring stable training. It is mathematically represented in equation (7). Actor adjusts portfolio weights; critic estimates value, refining both networks efficiently. That maximizes cumulative discounted reward; this formula is presented in equation (8).

(7)(8)

Allocation action is represented as is the market state. denotes the long-term portfolio performance, is the discount factor (0–1), is an immediate reward, and is mentioned as the Time step. is the next-period reward, is denoted as the future portfolio reward, and is the subsequent financial reward; is the future reward discount.

Evaluates how much better an action is compared to the average action, which is represented in equations (9) and (10). It updates policy parameters to increase the probability of better allocation decisions.

(9)(10)

is the policy gradient, is denoted as an advantage value, is an action value, is denoted as an action probability policy, and is the state value.

The Critic measures the quality and effectiveness of the Actor’s decisions. State value functions and State-action value functions are represented in equations (11) and (12). These functions evaluate whether the allocation decision improves expected financial return.

(11)(12)

is an expected state return, is an expected action return, and is a Policy expectation. TD Error is a mathematical derivation presented in equation (13). This error helps refine risk-adjusted return estimation during training.

(13)

Where denotes the Temporal Difference (TD) error, represents the immediate reward, is the discount factor for future rewards, denote the value functions of the next and current financial states, respectively, while represent the next and current intelligent finance states used in portfolio optimization learning. The Actor-Critic model is a dynamically optimizing model of portfolio weights that dynamically adjusts to non-stationary markets, accelerates convergence through parallel learning, trades off exploration and exploitation, and can reduce policy variance through advantage estimation to achieve stable performance. The DAC model improved on earlier models in the cumulative returns, risk-adjusted stability, robustness in volatile market conditions, convergence rate, and decisions on capital rebalancing, making it more adaptive toward a more realistic economic behavior.

Fig 2 demonstrates the DAC model of dynamic portfolio optimization. In this model, the Actor-Critic network is a combination of global networks, which provide information about the portfolio allocation based on parallel market simulation agents in various market conditions, such as volatility and stability. Based on TD error, the shared parameters are updated, and continuous strategy and assessment function updates are made to better allocate assets with time.

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Fig 2. DAC model for multiple agents interacting with market scenarios and shared network updates.

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2.4.2. CPPO for stabilizing and improving DAC learning performance.

CPPO is used to stabilize portfolio allocation changes in volatile financial market conditions. It controls portfolio adjustments by limiting the magnitude of policy updates during DAC training. The alleviate the overactive portfolio turnover, risk exposure due to instability, and convergence of non-stationary financial time series. In this proposed model, CPPO is employed as a policy stabilization layer on the top of the DAC policy, to prevent the sudden and overly aggressive real portfolio rebalancing decisions when the asynchronous actor policies updates. As a policy gradient reinforcement learning algorithm, traditional PPO maximizes a surrogate objective function derived from the probability ratio between the new policy and the current policy to regulate the training process. But from the perspective of a financial portfolio rebalancing problem, even PPO, the state-of-art contemporary algorithm, still introduces massive policy shifts under extreme market turbulence, which may destabilize the portfolio reallocation and adds financial risk to an impractical level. To comprehend this deficiency, the proposed CPPO incorporates a constrained clipping process, adapted to financial portfolio rebalancing task specifically, to maintain the weight updates in proportion to a pre-specified threshold bound when market variance becomes high. CPPO contorts the probability ratio within a preaged spectrum, avoiding any abrupt policy shifts or unstable rebalancing decisions, enhances the risk-adjusted returns, improves the portfolio's risk exposure, and bears better robustness in a finance market.

Maximizes the total long-term risk-adjusted cumulative returns with respect to the portfolio when the financial markets are in the presence of dynamic and unstable conditions. The form of the analytical expression is shown in Equation (14).

(14)

This ensures the model does not optimize only short-term profit but focuses on sustainable capital growth. It balances immediate reward and future financial stability using discount factor . is the state value, is denoted as the Expectation operator, is the Market state (price, MACD, volatility), is the summation of the overall response , is the Portfolio allocation weights, is the Risk-adjusted return, and the time step is represented as .

Measures allocation shift intensity between previous and updated portfolio decision policies. The formulation is presented in Equation (15).

(15)

The ratio of probabilities is defined as , where is the active policy, is the Previous policy, and is the policy parameters. Improves portfolio allocation toward higher advantage actions but may cause unstable weight updates. The formulation is presented in Equation (16).

(16)

is the Surrogate objective, is the batch expectation, and is an Advantage estimate. Restricts excessive portfolio weight updates to maintain financial stability under volatile and uncertain market environments. The detailed mathematical representation is given in Equation (17).

(17)

is the small threshold (e.g., 0.2), Stable convergence, reduced risk spikes, controlled rebalancing, and improved Sharpe ratio performance in practical evaluation. The Limits probability ratio range is mathematically represented in equation (18).

(18)

The Clipped objective is denoted as , is the Batch average, is the Probability ratio, is an advantage value, is the Clipping threshold, is the Conservative selection, is the denoted Ratio limiter. CPPO ensures controlled portfolio rebalancing by limiting excessive policy updates, reducing drawdown risk, improving learning stability, enhancing Sharpe ratio performance, and enabling adaptive capital allocation under non-stationary financial market conditions.

Fig 3 demonstrates the process of clipped PPO; the input data goes through the input embedding layer, processed by the policy and value networks. The actor decides on portfolio allocations, and the critic evaluates them based on past experience. CPPO ensures stable updates and improves the risk-adjusted return, ensuring that the model doesn't make drastic changes that could lead to instability.

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Fig 3. CPPO process for stable portfolio optimization and risk-adjusted return calculation.

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An intelligent portfolio allocation leverages a hybrid DAC-CPPO model that integrates DAC with CPPO for stable, risk-aware capital allocation. The Actor network dynamically generates portfolio weights, while the Critic estimates expected long-term returns, using temporal-difference errors and advantage functions to guide learning. DAC’s asynchronous parallel training improves convergence, balances exploration–exploitation, and adapts to non-stationary market conditions. CPPO constrains policy updates by limiting probability ratios between new and old policies, preventing excessive reallocations, controlling drawdown, and enhancing the Sharpe ratio performance. Combined, DAC-CPPO ensures adaptive, stable, and risk-adjusted portfolio management, achieving higher cumulative returns, reduced volatility exposure, and robust long-term capital growth under dynamic financial environments. Compared to traditional DRL portfolio methods such as standard Actor-Critic, DDPG, and PPO-based approaches, which often suffer from unstable policy updates, high variance, and sensitivity to market noise, the proposed DAC-CPPO model overcomes these limitations by introducing asynchronous multi-agent learning with clipped policy optimization, resulting in improved stability and better risk-adjusted performance.

An intelligent portfolio allocation framework is developed using the proposed DAC-CPPO architecture, which integrates DAC with CPPO to ensure stable and risk-aware capital allocation. Multiple worker agents interact with parallel financial environments and asynchronously update the global Actor–Critic networks. The Actor network generates allocation actions that determine portfolio weights, while the Critic estimates the value function to evaluate expected long-term returns. DAC layers normalize market states, extract latent features in hidden layers, generate risk-aware portfolio weights via the Actor Network, estimate returns with the Critic, and stabilize updates with CPPO. Advantage functions computed from temporal-difference errors guide policy learning. DAC’s asynchronous training improves convergence speed and enhances exploration in non-stationary financial markets. The CPPO objective constrains policy updates using probability-ratio clipping, preventing excessive portfolio reallocations and reducing drawdown risk. Unlike conventional DRL methods that directly update policies and may lead to unstable portfolio swings under volatile conditions, the proposed CPPO constraint ensures controlled and smooth rebalancing of assets. In turn, the DAC-CPPO model attains balanced weights of portfolio, better Sharpe ratio performance, lower volatility exposure, and strong long-term capital growth within fluctuating financial conditions. Fig 4 illustrates how the DAC-CPPO model is integrated to optimize a portfolio. The input environments (Env) are the financial market data and macroeconomic indicators, whereby the worker agents are subjected to varied market conditions. The agents produce portfolio weight, and the global actor-critic network optimizes the model with the CPPO constraint. The result is a stable allocation of risk-aware portfolio to market conditions.

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Fig 4. Proposed DAC-CPPO integration for stable portfolio optimization and risk management.

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Algorithm 1 demonstrates the Pseudocode for DAC-CPPO, the process of asynchronous Actor–Critic networks with CPPO to dynamically generate portfolio weights, optimizing risk-adjusted returns while controlling drawdowns and ensuring stable, adaptive capital allocation.

Algorithm 1: DAC-CPPO Reinforcement Learning for Portfolio Allocation

Input:

 Market states: s_t = [δ_t, w_t, l_t, x_t], Number of assets: D, Discount factor: γ ∈ (0,1)

 Transaction cost function: c(a_t, s_t), Learning rates: α_actor, α_critic, Clipping threshold: ε (e.g., 0.2), Investment horizon: T

Initialize Networks:

 - Actor μ(a_t|s_t; θ_a) with dense + LSTM layers

 - Critic V(s_t; θ_c) with dense + LSTM layers

 - Initialize global parameters and asynchronous workers

for t = 0 to T do

Actor chooses allocation weights

a_t ~ μ(a_t|s_t; θ_a)

Compute next-period wealth

x_(t + 1) = x_t * (w_t^T * δ_(t + 1) – c(a_t, s_t))

Compute risk-adjusted reward (Sharpe ratio)

r_t = μ_t / σ_t

Observe next state s_(t + 1)

Critic update: compute TD-error

θ_c ← θ_c + α_critic * δ_t * _θc V(s_t)

Actor update using the Advantage function

Adv(a_t, s_t) = Q(a_t, s_t) – V(s_t)

θ_a ← θ_a + α_actor * _θ L_CLIP(θ)

Update s_t ← s_(t + 1)

end for

end for

Return:

 Optimal policy π*(a_t|s_t) = argmax_πθ J(θ)

 Portfolio wealth trajectory x_t

Table 2 outlines key hyperparameters, their descriptions, and recommended value ranges to optimize training stability, exploration, and portfolio optimization performance in RL models.

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Table 2. Hyperparameters for DAC-CPPO model training.

https://doi.org/10.1371/journal.pone.0348010.t002

3.1. Intelligent portfolio allocation process

The proposed model of architecture of the intelligent portfolio allocation process, DAC-CPPO, is graphically visualized in Fig 5. It is a system that processes practical financial market data, performs state analysis and risk evaluation, and a hybrid Actor-Critic with CPPO engine is used to dynamically optimize the portfolio allocation in the non-stationary market conditions. Suggested DAC-CPPO optimization model of the dynamic portfolio and risk-sensitive allocation. It combines real-time market information (prices, volumes, volatility) and macroeconomic data to make informed portfolio choices. The DAC CPPO engine makes adjustments in the portfolio weights with feedback from the Performance Monitor and Risk Evaluation Engine. The Market State Analyzer identifies the trend and regime change, whereas the Dynamic Portfolio Allocator checks the real-time adjustments, giving the optimal use of assets under the risk.

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Fig 5. DAC-CPPO model for dynamic portfolio optimization and risk-aware allocation.

https://doi.org/10.1371/journal.pone.0348010.g005

The experimental approach used for the intelligent portfolio optimization model involved Intel i7 CPU with 32 GB RAM to achieve fast deep reinforcement learning model training. The proposed model DAC-CPPO was developed with the help of Python 3.10 programming language. First, historical datasets related to financial markets were split into training and testing datasets based on an 80:20 chronological division method to keep the order of observations from the real world. In addition, 5-fold expanding window time series cross-validation technique was applied to further verify the robustness and generalization of the model. In the process of applying this cross-validation scheme, the model was trained with the help of all historical observations up to a certain time point and tested on subsequent unseen period of time. As a result, the size of training window is increased after every iteration. In this way, the presented validation process ensures that there is no look-ahead bias present in the model, and a realistic estimation of convergence, risk-adjusted return, Sharpe ratio, and portfolio allocation can be achieved.

Fig 6 visualizes the distribution of normalized feature values of the different features of financial markets, where the lowest value is + 1.0 (high) and the highest value is −1.0 (low). The characteristics, including the Open Price, Simple Return, and Signal Line of the MACD, are rated, and the values of the various characteristics are represented by various colors. This visualization assists in acquiring knowledge about the spread and the variety of each of the features in the dataset, assisting in the selection of features to be used as models.

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Fig 6. Financial market feature distribution visualization with normalized feature value scales.

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Fig 7(a-b) illustrates the cumulative returns and drawdown of DAC-CPPO, DAC, PPO, and a benchmark model on 250 trading days. Fig 7(a) represents the cumulative returns of various models in 250 trading days. DAC-CPPO has an upward trend of returns, and it surpasses the DAC, PPO, and benchmark models. The Characteristics of the shaded area around the DAC-CPPO curve show the variability in the returns of the model, but it is the highest across the board, and this indicates the high level of effectiveness in portfolio management. Fig 7(b), a drawdown plot, puts the risk profile of DAC-CPPO into the limelight. This keeps DAC-CPPO at a minimum drawdown, unlike DAC and PPO, which can be near the zero point. This proves its capability to have minimal losses in times of market crashes; thus, it is more resilient than other models, especially in volatile trading times.

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Fig 7. Graphical Representation of the (a) Cumulative Return Comparison: DAC-CPPO outperforms other models in cumulative return (b) DAC-CPPO maintains lower drawdown compared to alternatives.

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Fig 8 gives a heatmap of the monthly Sharpe ratios of five models in relation to January to December. At deeper red colors, a higher Sharpe ratio is denoted. The DAC-CPPO model shows consistently good results of 2.05 in July, 2.16 in October, and 1.95 in September, which reflects better performance with respect to the risk-adjusted returns. By comparison, LSTM has its highest value of 2.17 in May but less stability in other months, whereas CPPO and DAC range between 0.85 and 1.69, which indicates mediocre performance. SVM also has significant variation, such as 2.11 in March and only 0.91 in December. On the whole, the steadiest and the highest Sharpe ratios all through the year are shown in DAC-CPPO and reflect its better ability to optimize the portfolio.

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Fig 8. Monthly sharpe ratio comparison across models (DAC-CPPO, DAC, PPO, LSTM, SVM).

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The role played by various factors in the ultimate Sharpe ratio of the DAC-CPPO model is shown in Fig 9. The greatest contribution goes to the Base Return of +0.80, then +0.25 of Risk Management. Sharpe ratio is gradually pushed up by using other parts like DAC Bonus, PPO Clip, and LDA Features. The efficiency of the model is proved by the last Sharpe ratio being 1.91.

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Fig 9. Component contributions to DAC-CPPO sharpe ratio for financial optimization.

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Fig 10 (a) visualizes the green candles to show an increase in price (closing price is higher than the opening price), and red candles to show a decrease in price (closing price is lower than the opening price). This is the price trend of every trading period. The volume subplot below the candlestick chart in Fig 10 (b) displays the volume of each session, and the bars in the plot are green and red, meaning higher buying volume and selling volume, respectively, which gives one an idea of the activity in the market in each trading period.

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Fig 10. Data features of stock prices for top 500 companies (a) stock price movements (b) trading activity levels.

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The Pearson correlation between different financial features and three types of Capital Action (Increase, Hold, and Decrease) is shown in this heatmap. Fig 11 shows the visualization of the heatmap. There are strong positive relationships with the LDA1, MACD, and Sharpe Ratio with the Increase class being observed, and they are thus important predictors. Contrarily, several features are negatively linked to “Decrease,” such as “Sentiment” and a “Sharpe_Ratio,” and reveal the inverse relations within the market trends.

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Fig 11. Features correlation heatmap with capital action classes in stock analysis.

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The arrangement of main characteristics of the stock market of the top 500 companies, mostly concentrating on data attributes, including Open, Close, High, Low, Volume, Dividends, and Stock Splits, with separate piecewise models of such companies as AAPL, MSFT, GOOGL, AMZN, and NVDA. This is depicted in Fig 12. The distribution of each feature is graphically obtained with time, and particularly how the price and trading conduct fluctuate amongst various companies. The analysis assists in evaluating the trends within the market and performance within the company.

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Fig 12. Stock market feature distribution for top 500 companies (price, volume).

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3.2. Comparative analysis

Table 3 provides the key measures and their formulas used to evaluate the performance of predictive models in this research. In this research, these metrics are applied to assess both prediction accuracy and the risk-aware decision quality of the proposed DAC-CPPO reinforcement learning model for optimal capital allocation in dynamic financial markets. Accuracy captures how accurate the market action sets are, and how well the model does at capturing the optimal action of an investment. Precision filters out false signals for profit while Recall captures the ability to identify all profitable signals. F1-Score balances the two for responsible decision making, while RMSE and MSE penalize for large errors in the predicted results, stabilizing performance in distressed market conditions. MAE measures the prediction average deviation for broad forecasting accuracy while MAPE measures based on percentage error comparisons between assets. R-Squared measures how well the model outperforms naive market models based on standard deviation of the financial return deviations.

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Table 3. Key evaluation metrics and formulas for model performance assessment.

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The DAC-CPPO algorithm is compared against two groups of reference algorithms. The first group consists of conventional ML and DL models (LR, RF, GB, SVM, LSTM, and Transformer), which are all directly applicable to financial forecasting and portfolio selection problems. The other group of algorithms is a set of financial sentiment models, i.e., FinBERT, BERT-base-uncased, RoBERTa-base, VADER, and TextBlob. The aforementioned sentiment models are used as indirect reference algorithms since they are extensively applied in intelligent investment frameworks for generating market sentiment that would later guide trading decisions. As the above-mentioned sentiment models were initially created to deal with financial text sentiment classification, not portfolio allocation/capital actions prediction per se, their performance can only serve as an indirect reference. Table 4 depicts the comparative performance of financial prediction techniques and sentiment analysis techniques along with the proposed DAC-CPPO model. Traditional machine learning techniques RF [30], LSTM [30], SVM [30], and GB [30] and deep learning models (Long Short-Term Memory and Transformer) act as baseline references for the financial prediction task, whereas, FinBERT, BERT-base-uncased, RoBERTa-base, VADER, and TextBlob act as financial sentiment analysis techniques which are frequently used with intelligent investment systems to help understand the market. These sentiment analysis techniques can be considered indirect reference baselines due to the fact that they do not directly allocate capital like the proposed DAC-CPPO model. The proposed DAC-CPPO model outperforms all other baseline techniques with the best accuracy (97.6%), precision (97.1%), recall (96.5%), F1-score (96.9%), and AUC-ROC (0.984).

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Table 4. Comparative performance of ML approaches and the proposed DAC-CPPO model.

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Table 4 offers the comparison results of several sentiment analysis and machine learning schemes to perform financial prediction tasks. Conventional algorithms like VADER [29] and TextBlob [29] are not as efficient since they do not have much understanding of their context. Moderate improvements are made by classical ML models such as LR [30], RF [30], GB [30], SVM [30], etc. DL models such as LSTM [30] and Transformer architecture substantially improve prediction accuracy and classification reliability. The proposed DAC-CPPO model achieves the highest performance across all metrics, demonstrating superior accuracy (97.6%), precision (97.1%), recall (96.5%), F1-score (96.9%), and an AUC-ROC of 0.984 for intelligent financial sentiment. The comparison between the suggested DAC-CPPO algorithm and classical machine learning or deep learning methods which directly aim at financial forecasting is presented in Fig 13. The comparative illustration for the case of indirect comparison with models which are used for financial sentiment analysis and are applied in the intelligent investment pipeline is depicted in Fig 14.

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Fig 13. Performance comparison of existing models [30] and proposed DAC-CPPO visualization results.

https://doi.org/10.1371/journal.pone.0348010.g013

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Fig 14. Visualization performance comparison of existing models [29] and proposed DAC-CPPO model.

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Fig 14 shows the performance comparison of the selected financial sentiment analysis methods that include FinBERT, BERT-base-uncased, RoBERTa-base [29], VADER [29], and TextBlob [29] along with the proposed DAC-CPPO method. The models mainly do financial sentiment classification and thus function as indirect reference baseline algorithms rather than direct portfolio allocation strategies. Their representation serves to show the potential of financial sentiment-based intelligence methods compared to other intelligent investing systems while DAC-CPPO is focused on capital allocation through reinforcement learning. The relative performance of FinBERT, BERT-base-uncased, RoBERTa-base, VADER, TextBlob, and the suggested DAC-CPPO model is depicted in Fig 14, which shows that the suggested model gives the best performance among all the metrics used. Table 5 provides the Comparative evaluation of error metrics, showing improved prediction accuracy and reliability of the proposed DAC-CPPO model against traditional, machine learning, and deep learning approaches.

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Table 5. Comparison of error metrics across various models with the proposed DAC-CPPO model.

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Table 5 and Fig 15 indicate the performance measure of different techniques, such as Traditional models [28], tree-based models like Random Forest and Decision Tree, which are conventional machine learning algorithms used as baseline methods for performance comparison, RF [30], SVM [30], LSTM [30], and Transformer. The DAC-CPPO model is the best in terms of the lowest MAE (0.074), MSE (0.013), and the RMSE (0.081), which means that the prediction accuracy is high. The model also has good performance, as indicated in its MAPE (4.6) and R-squared (0.985); it has the potential to maximize risk-adjusted returns and minimize the level of mistakes made in forecasting the portfolio in relation to other models. All experiments are conducted using a 5-year historical financial dataset covering market records from the Massive Yahoo Finance dataset, ensuring long-term market dynamics are captured for robust evaluation.

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Fig 15. Visualization of prediction error metrics comparing existing models and proposed DAC-CPPO framework performance.

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The comparative transaction of Sharpe ratios under different models is listed in Table 6 and Fig 16, indicating the excellence of the suggested DAC-CPPO. Sharpe ratio is a ratio that is used in measuring portfolio risk-adjusted returns, which measures excess returns per unit increase in volatility, whereby higher values imply excellent performance, enhanced efficiency, and also enhanced investment stability. The Sharpe ratio is computed using the following equation (19).

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Table 6. Comparison of sharpe ratios for various models and proposed DAC-CPPO framework.

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Fig 16. Comparative sharpe ratio performance of financial models and proposed DAC-CPPO framework.

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(19)

where denotes the annualized Sharpe ratio, is the average daily portfolio return, is the annual risk-free rate, and is the standard deviation of daily portfolio returns. The Sharpe ratio was computed using daily portfolio returns and annualized using 252 trading days according to . An annual risk-free rate of 2% (0.02) was adopted throughout all experiments. The same Sharpe ratio calculation procedure was consistently applied to the proposed DAC-CPPO model and all baseline methods to ensure fair comparison across Table 6 and Fig 16.

All Sharpe ratios used here are annual numbers, calculated using the daily returns of the portfolio on 252 trading days per year with an annual risk-free rate of 2% (0.02).

These reported Sharpe ratios are annualized ratios that have been calculated from daily returns for each portfolio with 252 trading days and an annual risk-free rate of 2% (0.02). The performance comparison of various traditional ML, DL, and DRL models for intelligent capital allocation is presented in Table 7. All models, including DQN [27], Traditional methods, SVM [28], FinBERT, BERT-base-uncased, VADER [29], LR, RF, GB, LSTM, Transformer [30], and the proposed DAC-CPPO method, were implemented and trained using two benchmark datasets: the Intelligent Finance Assets dataset and the Massive Yahoo Finance dataset, ensuring a fair and consistent evaluation environment across all approaches. The results demonstrate that traditional sentiment and statistical models, such as VADER and Logistic Regression, achieve comparatively lower performance due to their limited capability in capturing complex nonlinear financial dependencies. Machine learning models such as SVM, RF, and GB show improved predictive ability, while deep learning architectures, including LSTM and Transformer models, further enhance performance by effectively modeling sequential financial patterns. The DRL-based DQN model demonstrates better decision-making capability compared to classical ML and DL models, highlighting the advantage of reinforcement learning in dynamic financial environments.

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Table 7. Comparative performance of ML and DL techniques on financial datasets for capital allocation.

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Table 7 provides that the proposed DAC-CPPO model significantly outperforms all baseline approaches by achieving the highest Accuracy (97.6%), Precision (97.1%), Recall (96.5%), and F1-Score (96.9%). This improvement enhances policy stability, exploration efficiency, and risk-sensitive decision-making. Overall, the results confirm that the proposed DAC-CPPO method provides superior adaptability, robustness, and risk-adjusted performance for intelligent capital allocation in volatile financial markets.

3.3. Class-wise performance analysis

Despite the proposed DAC-CPPO model having an overall accuracy of 97.6%, it is still necessary to conduct a further class-level test to confirm that the model is equally effective for all the portfolio decision-making classes. The test was done using the chronological testing set in which the portfolio decisions were classified as Increase, Hold, and Decrease. Precision, recall, and F1-score of each class were considered together with the confusion matrix.

As shown in Fig 17, the classification is quite good for all three portfolio actions. In case of actual “Increase” actions, there are 4 correct classifications while 1 is misclassified as “Hold”. In case of actual “Hold” actions, there are 3 correct classifications, with 1 being misclassified as “Increase” action and another 1 as “Decrease” action.

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Fig 17. Confusion matrix of the proposed DAC-CPPO model for portfolio action classification.

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3.4. Ablation research

The ablation research assesses the impact of every building block of architecture on the experimental results. Preprocessing, feature extraction, DAC learning, and CPPO stabilization are presented results respectively by turn. Results indicate that reinforcement learning parts has contributed to the security of financial decision stability, the ability of risk control, and the efficiency of rate of return. Ablation research results signify that the architecture of DAC-CPPO configuration can balance the risk adjusted return performance and the prediction accuracy better. The contribution of preprocessing, feature extraction, DAC and CPPO is illustrated in Table 8.

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Table 8. Ablation analysis of proposed DAC-CPPO framework for intelligent portfolio allocation.

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Table 8 presents an ablation analysis evaluating the contribution of each component in the proposed framework. Starting with only preprocessing, performance gradually improves as feature extraction, DAC learning, and CPPO stabilization are added. Each additional module increases cumulative return and Sharpe ratio while reducing volatility. The complete DAC-CPPO model achieves the best results with 1.12 cumulative return, 1.91 Sharpe ratio, and 97.6% accuracy.

3.5. Time-series cross-validation analysis

To perform a statistically sound validation that takes into account the chronological nature of the financial market data set, the DAC-CPPO framework was validated using an approach of 5-fold expanding window time-series cross-validation. Unlike traditional random k-fold cross-validation, which introduces the problem of look-ahead bias through the inclusion of future observations in the training set, the used validation method preserves the temporal ordering for all the folds. In each round of the algorithm, the model was trained with all the historical observations and tested on the following unseen time segment. After the completion of each fold, the training set was extended with the previous testing observation before performing the test for the next unseen time interval. This validation method represents the actual approach of portfolio management, in which investment is performed only on the basis of the historical data. The average performance of the proposed model on the validation folds was reported using mean, SD, 95% CI and paired t-test is represented as Table 9.

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Table 9. Cross-validation performance evaluation of DAC-CPPO model for reinforcement learning-driven optimal capital allocation in intelligent finance.

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The performance results for the suggested DAC-CPPO model through the execution of the 5-fold expanding window time series cross-validation method are provided in Table 9. The model managed to score a mean accuracy of 97.4%, a precision of 97.0%, a recall of 96.2%, and an F1-score of 96.5%. This shows that the proposed model has reliable prediction capabilities regardless of the chronological partitioning of the financial market. The small standard deviation and the tight 95% confidence intervals show that the generalization ability of the proposed model does not change with each consecutive partitioning of the financial market data. In addition, the p-value from the paired t-test is less than 0.001, which demonstrates statistical significance in the improvement.

3.6. Discussion

The discussion section evaluating the proposed DAC-CPPO model with better portfolio allocation performance, higher risk-adjusted return, lower volatility and more reliable decision stability is to make far more explicit. limitations of most existing portfolio allocation models. Big data finance models increase the utilization of information; however, they are highly susceptible to the quality and infrastructure of data (lowering the resilience in practice). The model design proposed implements the preprocessing (data normalization, data cleaning, LDA) to produce robust inputs. Carbide clustering models are also optimized by IoT schemes to enhance segmentation, but do not directly optimize risk-adjusted optimization, which constrains financial learning effectiveness; DAC-CPPO is a direct maximization of long-term Sharpe goals, risk-sensitive capital allocation. Traditional DRA methods can be weak in terms of risk adjustment, with respect to using non-stationary markets, and residential to unstable allocations are acquired in situations where tail risk is present [28]; the suggested DAC-CPPO framework combines risk-sensitive rewards and clipped updates to bring about a high-quality decision. Sentiment enhancement DRL models are expressive, but have high computational complexity and low multi-asset generalization [29]. The model algorithm proposed here trades expressivity and scalable policy learning. Third, traditional machine learning systems can provide predictive accuracy but no dynamic feedback control, which undermines adaptive allocation [30]; DAC-CPPO was an actor-critic system, where the weights are always updated. The proposed model of DAC-CPPO has feasible benefits in introducing smart capital allocation to the changing financial market. It assists in balancing the exploration of the DAC as well as that of maintenance of the policy, which comprises the adaptive rebalancing of the portfolio, risk-adjusted returns, and exposure to volatility. Financial institutions and asset managers can use this approach to enhance automated investment processes, capital allocation, and provide information-based finance decisions.

The high accuracy rate obtained using the DAC-CPPO framework needs to be understood in conjunction with the evaluation methodology used. The problem of financial time series forecasting is intrinsically difficult due to factors such as market volatility, temporal dependencies, and non-stationarity. To have a proper evaluation, train-test splits were performed chronologically and no feature extraction used observations beyond those available at each point prior to forecasting. Also, class-wise analysis reveals reliable forecasting capabilities for the Increase, Hold, and Decrease portfolio decisions, and not just one dominant class. Such evaluations are evidence that the results obtained indicate good learning abilities of the proposed framework for portfolio decision-making in dynamic financial markets and not just luck of data leakage or an easy classification problem.