We propose DeepAries , a novel deep reinforcement learning framework for dynamic portfolio management that jointly optimizes the timing and allocation of rebalancing decisions. Unlike prior reinforcement learning methods that employ fixed rebalancing intervals regardless of market conditions, DeepAries adaptively selects optimal rebalancing intervals along with portfolio weights to reduce unnecessary transaction costs and maximize risk-adjusted returns. Our framework integrates a Transformer-based state encoder, which effectively captures complex long-term market dependencies, with Proximal Policy Optimization (PPO) to generate simultaneous discrete (rebalancing intervals) and continuous (asset allocations) actions. Extensive experiments on multiple real-world financial markets demonstrate that DeepAries significantly outperforms traditional fixed-frequency and full-rebalancing strategies in terms of risk-adjusted returns, transaction costs, and drawdowns. Additionally, we provide a live demo of DeepAries at https://deep-aries.github.io/, along with the source code and dataset at https://github.com/dmis-lab/DeepAries, illustrating DeepAries' capability to produce interpretable rebalancing and allocation decisions aligned with shifting market regimes. Overall, DeepAries introduces an innovative paradigm for adaptive and practical portfolio management by integrating both timing and allocation into a unified decision-making process.

Statistical arbitrage exploits temporal price differences between similar assets. We develop a framework to jointly identify similar assets through factors, identify mispricing and form a trading policy that maximizes risk-adjusted performance after trading costs. Our Attention Factors are conditional latent factors that are the most useful for arbitrage trading. They are learned from firm characteristic embeddings that allow for complex interactions. We identify time-series signals from the residual portfolios of our factors with a general sequence model. Estimating factors and the arbitrage trading strategy jointly is crucial to maximize profitability after trading costs. In a comprehensive empirical study we show that our Attention Factor model achieves an out-of-sample Sharpe ratio above 4 on the largest U.S. equities over a 24-year period. Our one-step solution yields an unprecedented Sharpe ratio of 2.3 net of transaction costs. We show that weak factors are important for arbitrage trading.

Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for optimal portfolio choice. To address this question, we parameterize minimum-variance portfolio weights as a function of a large pool of firm-level characteristics as well as their second-order and cross-product transformations, yielding a total of 4,610 predictors. We find that the gains from employing ML to select relevant predictors are substantial: minimum-variance portfolios achieve lower risk relative to sparse specifications commonly considered in the literature, especially when non-linear terms are added to the predictor space. Moreover, some of the selected predictors that help decreasing portfolio risk also increase returns, leading to minimum-variance portfolios with good performance in terms of Shape ratios in some situations. Our evidence suggests that ad-hoc sparsity can be detrimental to the performance of minimum-variance characteristics-based portfolios.

This paper addresses the critical disconnect between prediction and decision quality in portfolio optimization by integrating Large Language Models (LLMs) with decision-focused learning. We demonstrate both theoretically and empirically that minimizing the prediction error alone leads to suboptimal portfolio decisions. We aim to exploit the representational power of LLMs for investment decisions. An attention mechanism processes asset relationships, temporal dependencies, and macro variables, which are then directly integrated into a portfolio optimization layer. This enables the model to capture complex market dynamics and align predictions with the decision objectives. Extensive experiments on S\&P100 and DOW30 datasets show that our model consistently outperforms state-of-the-art deep learning models. In addition, gradient-based analyses show that our model prioritizes the assets most crucial to decision making, thus mitigating the effects of prediction errors on portfolio performance. These findings underscore the value of integrating decision objectives into predictions for more robust and context-aware portfolio management.

Deep Reinforcement Learning (DRL) has been extensively used to address portfolio optimization problems. The DRL agents acquire knowledge and make decisions through unsupervised interactions with their environment without requiring explicit knowledge of the joint dynamics of portfolio assets. Among these DRL algorithms, the combination of actor-critic algorithms and deep function approximators is the most widely used DRL algorithm. Here, we find that training the DRL agent using the actor-critic algorithm and deep function approximators may lead to scenarios where the improvement in the DRL agent's risk-adjusted profitability is not significant. We propose that such situations primarily arise from the following two problems: sparsity in positive reward and the curse of dimensionality. These limitations prevent DRL agents from comprehensively learning asset price change patterns in the training environment. As a result, the DRL agents cannot explore the dynamic portfolio optimization policy to improve the risk-adjusted profitability in the training process. To address these problems, we propose a novel multi-agent Hierarchical Deep Reinforcement Learning (HDRL) algorithmic framework in this research. Under this framework, the agents work together as a learning system for portfolio optimization. Specifically, by designing an auxiliary agent that works together with the executive agent for optimal policy exploration, the learning system can focus on exploring the policy with higher risk-adjusted return in the action space with positive return and low variance. In this way, we can overcome the issue of the curse of dimensionality and improve the training efficiency in the positive reward sparse environment.

In equity markets, stocks are conventionally labeled by equity indices (company names). By relabeling stocks according to their ranks in capitalization, rather than their equity indices (company names), a different, more stable market structure can emerge. Specifically, we will gain a different perspective on market dynamics by focusing on the stock that occupies a certain rank in capitalization while the corresponding company name may change. We refer to a market labeled by the equity indices (company names) as a market in name space and one labeled by ranks in capitalization as a market in rank space . Market in rank space was explored by Fernholtz et al. who observed a stable distribution of capitalization across different ranks in the U.S. equity market over different time periods [11,16]. They further introduced an explanatory hybrid-Atlas model under stochastic portfolio theory, a framework that enables analyzing portfolios in rank space [5,15]. Empirically, B. Healy et al. analyzed the U.S. equity data and showed that the market in rank space is driven by a dominant single factor [14], in contrast to the multi-factor-driven market in name space [9,10,19]. While the primary market factor in rank space has been extensively studied, the residual returns - those not explained by this primary factor in stock returns - remain a fertile land of adventure.

Portfolio management is the art and science in fiance that concerns continuous reallocation of funds and assets across financial instruments to meet the desired returns to risk profile. Deep reinforcement learning (RL) has gained increasing interest in portfolio management, where RL agents are trained base on financial data to optimize the asset reallocation process. Though there are prior efforts in trying to combine RL and portfolio management, previous works did not consider practical aspects such as transaction costs or short selling restrictions, limiting their applicability. To address these limitations, we propose a general RL framework for asset management that enables continuous asset weights, short selling and making decisions with relevant features. We compare the performance of three different RL algorithms: Policy Gradient with Actor-Critic (PGAC), Proximal Policy Optimization (PPO), and Evolution Strategies (ES) and demonstrate their advantages in a simulated environment with transaction costs. Our work aims to provide more options for utilizing RL frameworks in real-life asset management scenarios and can benefit further research in financial applications.

We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behaviour, shapes, number of modes, etc., of the resulting weight adjusted empirical distribution. In this article, we substantially enhance the flexibility of such methodology by introducing a nonparametrically imbued distributional constraints on the weights, and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric while allowing for subtle departures. The versatility of the framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task: namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms.

Many cryptocurrency brokers nowadays offer a variety of derivative assets that allow traders to perform hedging or speculation. This paper proposes an effective algorithm based on neural networks to take advantage of these investment products. The proposed algorithm constructs a portfolio that contains a pair of negatively correlated assets. A deep neural network, which outputs the allocation weight of each asset at a time interval, is trained to maximize the Sharpe ratio. A novel loss term is proposed to regulate the network's bias towards a specific asset, thus enforcing the network to learn an allocation strategy that is close to a minimum variance strategy. Extensive experiments were conducted using data collected from Binance spanning 19 months to evaluate the effectiveness of our approach. The backtest results show that the proposed algorithm can produce neural networks that are able to make profits in different market situations.

We propose the first discrete-time infinite-horizon dynamic formulation of the financial index tracking problem under both return-based tracking error and value-based tracking error. The formulation overcomes the limitations of existing models by incorporating the intertemporal dynamics of market information variables not limited to prices, allowing exact calculation of transaction costs, accounting for the tradeoff between overall tracking error and transaction costs, allowing effective use of data in a long time period, etc. The formulation also allows novel decision variables of cash injection or withdraw. We propose to solve the portfolio rebalancing equation using a Banach fixed point iteration, which allows to accurately calculate the transaction costs specified as nonlinear functions of trading volumes in practice. We propose an extension of deep reinforcement learning (RL) method to solve the dynamic formulation. Our RL method resolves the issue of data limitation resulting from the availability of a single sample path of financial data by a novel training scheme. A comprehensive empirical study based on a 17-year-long testing set demonstrates that the proposed method outperforms a benchmark method in terms of tracking accuracy and has the potential for earning extra profit through cash withdraw strategy.