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This article presents a deep reinforcement learning approach to price and hedge financial derivatives. This approach extends the work of Guo and Zhu (2017) who recently introduced the equal risk pricing framework, where the price of a…

Computational Finance · Quantitative Finance 2020-06-09 Alexandre Carbonneau , Frédéric Godin

The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in…

Computational Finance · Quantitative Finance 2021-07-26 Alexandre Carbonneau , Frédéric Godin

This study presents a deep reinforcement learning approach for global hedging of long-term financial derivatives. A similar setup as in Coleman et al. (2007) is considered with the risk management of lookback options embedded in guarantees…

Risk Management · Quantitative Finance 2020-07-31 Alexandre Carbonneau

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…

Optimization and Control · Mathematics 2020-09-17 Saeed Marzban , Erick Delage , Jonathan Yumeng Li

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We…

Computational Finance · Quantitative Finance 2018-02-12 Hans Bühler , Lukas Gonon , Josef Teichmann , Ben Wood

Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…

Computational Finance · Quantitative Finance 2025-03-07 Yiheng Ding , Gangnan Yuan , Dewei Zuo , Ting Gao

We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying…

Portfolio Management · Quantitative Finance 2025-12-16 Travon Lucius , Christian Koch , Jacob Starling , Julia Zhu , Miguel Urena , Carrie Hu

In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…

Computational Finance · Quantitative Finance 2025-11-27 Nicolas Baradel

Deep hedging is a framework for hedging derivatives in the presence of market frictions. In this study, we focus on the problem of hedging a given target option by using multiple options. To extend the deep hedging framework to this…

Computational Finance · Quantitative Finance 2023-05-23 Masanori Hirano , Kentaro Imajo , Kentaro Minami , Takuya Shimada

This work focuses on the dynamic hedging of financial derivatives, where a reinforcement learning algorithm is designed to minimize the variance of the delta hedging process. In contrast to previous research in this area, we apply…

Optimization and Control · Mathematics 2023-06-21 Cong Zheng , Jiafa He , Can Yang

We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which…

Computational Finance · Quantitative Finance 2025-04-24 Fabienne Schmid , Daniel Oeltz

In this paper, we explore the pricing and hedging strategies for an innovative insurance product called the equity protection swap(EPS). Notably, we focus on the application of EPSs involving cross-currency reference portfolios, reflecting…

Mathematical Finance · Quantitative Finance 2026-04-10 Marek Rutkowski , Huansang Xu

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and…

Computational Finance · Quantitative Finance 2021-03-31 Jay Cao , Jacky Chen , John Hull , Zissis Poulos

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement…

Computational Finance · Quantitative Finance 2024-02-26 Andrei Neagu , Frédéric Godin , Clarence Simard , Leila Kosseim

Recently equal risk pricing, a framework for fair derivative pricing, was extended to consider dynamic risk measures. However, all current implementations either employ a static risk measure that violates time consistency, or are based on…

Pricing of Securities · Quantitative Finance 2021-09-10 Saeed Marzban , Erick Delage , Jonathan Yumeng Li

Deep hedging is a deep-learning-based framework for derivative hedging in incomplete markets. The advantage of deep hedging lies in its ability to handle various realistic market conditions, such as market frictions, which are challenging…

Computational Finance · Quantitative Finance 2023-07-26 Masanori Hirano , Kentaro Minami , Kentaro Imajo

This paper studies the valuation of European contingent claims with short selling bans under the equal risk pricing (ERP) framework proposed in Guo and Zhu (2017) where analytical pricing formulae were derived in the case of monotonic…

Mathematical Finance · Quantitative Finance 2021-08-27 Guiyuan Ma , Song-Ping Zhu , Ivan Guo

The trade off between risks and returns gives rise to multi-criteria optimisation problems that are well understood in finance, efficient frontiers being the tool to navigate their set of optimal solutions. Motivated by the recent advances…

Computational Finance · Quantitative Finance 2021-04-13 Zheng Gong , Carmine Ventre , John O'Hara

This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…

Computational Finance · Quantitative Finance 2023-10-09 Zoran Stoiljkovic

Research in quantitative finance has demonstrated that reinforcement learning (RL) methods have delivered promising outcomes in the context of hedging financial portfolios. For example, hedging a portfolio of European options using RL…

Computational Engineering, Finance, and Science · Computer Science 2024-07-16 Anil Sharma , Freeman Chen , Jaesun Noh , Julio DeJesus , Mario Schlener
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