Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 4

WP(31/2026)525. Co-adaptation: From MARL Non-stationarity to the Dynamics of Economic Adjustment

Authors: Lisicki Jan, Kopczewski Tomasz
Economic agents adapt their behavior to experience generated by interactions with other market participants. When several agents update their behavioral rules simultaneously, these adaptation processes become interdependent. We refer to this mechanis…

WP525. Co-adaptation: From MARL Non-stationarity to the Dynamics of Economic Adjustment

Economic agents adapt their behavior to experience generated by interactions with other market participants. When several agents update their behavioral rules simultaneously, these adaptation processes become interdependent. We refer to this mechanism 
as co-adaptation. The paper develops a formal representation that separates the continuation of an agent's own rule updates from cross-agent effects on subsequent updates. In a two-agent system, mutual influence can increase the cumulative effect of an initial change and prolong the resulting adjustment process. A simple model of price adjustment between two firms shows how these effects depend on adjustment speed and the response to a competitor's price change. With more agents, interdependencies between adaptation processes form a directed network. This perspective links economic adjustment to multi-agent reinforcement learning, where learning by one agent changes the environment experienced by others, and clarifies when such non-stationarity is part of economic dynamics rather than only a computational difficulty.


DOI: https://doi.org/10.33138/2957-0506.2026.31.525
Lisicki Jan, Kopczewski Tomasz
economic adjustment multi-agent reinforcement learning adaptive learning agent-based computational economics co-adaptation

WP(25/2025)488. Application of Deep Reinforcement Learning to At-the-Money S&P 500 Options Hedging

Authors: Bracha Zofia, Michańków Jakub, Sakowski Paweł
This paper explores the application of deep Q-learning to hedging at-the-money options on the S&P 500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions w…

WP488. Application of Deep Reinforcement Learning to At-the-Money S&P 500 Options Hedging

This paper explores the application of deep Q-learning to hedging at-the-money options on the S&P 500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions without making explicit model assumptions on price dynamics. The agent was trained on historical intraday prices of S&P 500 call options across years 2004 to 2024, using a single time series of six predictor variables: option price, underlying asset price, moneyness, time to maturity, realized volatility, and current hedge position. A walk-forward procedure was applied for training, which lead to nearly 17 years of out-of-sample evaluation. The performance of the deep reinforcement learning (DRL) agent is benchmarked against the Black–Scholes delta hedging strategy over the same time period. We assess both approaches using metrics such as annualized return, volatility, information ratio, and Sharpe ratio. To test models’ adaptability, we performed simulations across varying market conditions and added constraints such as transaction costs and risk-awareness penalties. Our results show that the DRL agent can outperform traditional hedging methods, particularly in volatile or high-cost environments, highlighting its robustness and flexibility in practical trading contexts. While the agent consistently outperforms delta hedging, its performance deteriorates when the risk-awareness parameter is higher. We also observed that the longer the time interval used for volatility estimation, the more stable the results.


DOI: https://doi.org/10.33138/2957-0506.2025.25.488
Bracha Zofia, Michańków Jakub, Sakowski Paweł
Deep learning Reinforcement learning Double Deep Q-netwoorks options market options hedging deep hedging

WP(22/2025)485. A survey of statistical arbitrage pair trading with machine learning, deep learning, and reinforcement learning methods

Authors: Sun Yufei
Pair trading remains a cornerstone strategy in quantitative finance, having consistently attracted scholarly attention from both economists and computer scientists. Over recent decades, research has expanded beyond traditional linear frameworks&mdash…

WP485. A survey of statistical arbitrage pair trading with machine learning, deep learning, and reinforcement learning methods

Pair trading remains a cornerstone strategy in quantitative finance, having consistently attracted scholarly attention from both economists and computer scientists. Over recent decades, research has expanded beyond traditional linear frameworks—such as regression- and cointegration-based models—to embrace advanced methodologies, including machine learning (ML), deep learning (DL), reinforcement learning (RL), and deep reinforcement learning (DRL). These techniques have demonstrated superior capacity to capture nonlinear dependencies and complex dynamics in financial data, thereby enhancing predictive performance and strategy design.
Building on these academic developments, practitioners are increasingly deploying DL models to forecast asset price movements and volatility in equity and foreign exchange markets, leveraging the advantages of artificial intelligence (AI) for trading. In parallel, DRL has gained prominence in algorithmic trading, where agents can autonomously learn optimal trading policies by interacting with market environments, enabling systems that move beyond price prediction to dynamic signal generation and portfolio allocation.
This paper provides a comprehensive survey of ML-, DL-, RL-, and DRL-based approaches to pair trading within quantitative finance. By systematically reviewing existing studies and highlighting their methodological contributions, it offers researchers a structured foundation for replication and further development. In addition, the paper outlines promising avenues for future research that extend the application of AI-driven methods in statistical arbitrage and market microstructure analysis.


DOI: https://doi.org/10.33138/2957-0506.2025.22.485
Sun Yufei
Pair Trading Machine Learning Deep Learning Reinforcement Learning Deep Reinforcement Learning Artificial Intelligence Quantitative Trading

WP(14/2025)477. Can Artificial Intelligence Trade the Stock Market?

Authors: Jędrzej Maskiewicz, Sakowski Paweł
The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these…

WP477. Can Artificial Intelligence Trade the Stock Market?

The paper explores the use of Deep Reinforcement Learning (DRL) in stock market trading, focusing on two algorithms: Double Deep Q-Network (DDQN) and Proximal Policy Optimization (PPO) and compares them with Buy and Hold benchmark. It evaluates these algorithms across three currency pairs, the S&P 500 index and Bitcoin, on the daily data in the period of 2019-2023. The results demonstrate DRL's effectiveness in trading and its ability to manage risk by strategically avoiding trades in unfavorable conditions, providing a substantial edge over classical approaches, based on supervised learning in terms of risk-adjusted returns.


DOI: https://doi.org/10.33138/2957-0506.2025.14.477
Jędrzej Maskiewicz, Sakowski Paweł
Reinforcement Learning Deep Learning stock market algorithmic trading Double Deep Q-Network Proximal Policy Optimization
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