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We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the…

Computational Finance · Quantitative Finance 2023-11-22 Ali Fathi , Bernhard Hientzsch

This paper contributes to the existing literature on hedging American options with Deep Reinforcement Learning (DRL). The study first investigates hyperparameter impact on hedging performance, considering learning rates, training episodes,…

Risk Management · Quantitative Finance 2024-05-15 Reilly Pickard , F. Wredenhagen , Y. Lawryshyn

Dynamic hedging is a financial strategy that consists in periodically transacting one or multiple financial assets to offset the risk associated with a correlated liability. Deep Reinforcement Learning (DRL) algorithms have been used to…

Computational Finance · Quantitative Finance 2025-04-18 Andrei Neagu , Frédéric Godin , Leila Kosseim

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…

Computational Finance · Quantitative Finance 2025-10-13 Zofia Bracha , Paweł Sakowski , Jakub Michańków

This article leverages deep reinforcement learning (DRL) to hedge American put options, utilizing the deep deterministic policy gradient (DDPG) method. The agents are first trained and tested with Geometric Brownian Motion (GBM) asset paths…

Risk Management · Quantitative Finance 2024-05-14 Reilly Pickard , Finn Wredenhagen , Julio DeJesus , Mario Schlener , Yuri Lawryshyn

In this work we deal with the funding costs rising from hedging the risky securities underlying a target volatility strategy (TVS), a portfolio of risky assets and a risk-free one dynamically rebalanced in order to keep the realized…

Pricing of Securities · Quantitative Finance 2021-12-06 Roberto Daluiso , Emanuele Nastasi , Andrea Pallavicini , Stefano Polo

We propose a new risk sensitive reinforcement learning approach for the dynamic hedging of options. The approach focuses on the minimization of the tail risk of the final P&L of the seller of an option. Different from most existing…

Risk Management · Quantitative Finance 2024-11-15 Xianhua Peng , Xiang Zhou , Bo Xiao , Yi Wu

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

Traditional portfolio management methods can incorporate specific investor preferences but rely on accurate forecasts of asset returns and covariances. Reinforcement learning (RL) methods do not rely on these explicit forecasts and are…

Portfolio Management · Quantitative Finance 2022-03-23 Ruan Pretorius , Terence van Zyl

This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time…

Computational Finance · Quantitative Finance 2019-09-04 Igor Halperin

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

The deployment of autonomous AI agents in derivatives markets has widened a practical gap between static model calibration and realized hedging outcomes. We introduce two reinforcement learning frameworks, a novel Replication Learning of…

Artificial Intelligence · Computer Science 2026-03-10 Minxuan Hu , Ziheng Chen , Jiayu Yi , Wenxi Sun

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

This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these…

Computational Finance · Quantitative Finance 2024-08-27 Chunhui Qiao , Xiangwei Wan

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 this paper we show how risk-averse reinforcement learning can be used to hedge options. We apply a state-of-the-art risk-averse algorithm: Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment, considering…

Trading and Market Microstructure · Quantitative Finance 2020-10-26 Edoardo Vittori , Michele Trapletti , Marcello Restelli

We extend the Q-learner in Black-Scholes (QLBS) framework by incorporating risk aversion and trading costs, and propose a novel Replication Learning of Option Pricing (RLOP) approach. Both methods are fully compatible with standard…

Pricing of Securities · Quantitative Finance 2026-01-06 Ziheng Chen , Minxuan Hu , Jiayu Yi , Wenxi Sun

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

The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning…

Computational Finance · Quantitative Finance 2023-12-27 David Wu , Sebastian Jaimungal

We proposed a new Portfolio Management method termed as Robust Log-Optimal Strategy (RLOS), which ameliorates the General Log-Optimal Strategy (GLOS) by approximating the traditional objective function with quadratic Taylor expansion. It…

Portfolio Management · Quantitative Finance 2018-05-02 Yifeng Guo , Xingyu Fu , Yuyan Shi , Mingwen Liu
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