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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

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

Reinforcement learning has become one of the best approach to train a computer game emulator capable of human level performance. In a reinforcement learning approach, an optimal value function is learned across a set of actions, or…

Machine Learning · Computer Science 2019-08-22 Jeremy Charlier , Gaston Ormazabal , Radu State , Jean Hilger

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

This paper presents a novel way to apply mathematical finance and machine learning (ML) to forecast stock options prices. Following results from the paper Quasi-Reversibility Method and Neural Network Machine Learning to Solution of…

Statistical Finance · Quantitative Finance 2022-12-13 Zheng Cao , Wenyu Du , Kirill V. Golubnichiy

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

We proposed classification models that utilize the result from the Quasi-Reversibility Method, which solves the Black-Scholes equation to forecast the option prices one day in advance. Combining the minimizer from QRM with our machine…

Optimization and Control · Mathematics 2025-01-28 Benjamin Jiang , Matthieu Durieux , Kirill V. Golubnichiy

Abstract In this work, we build two environments, namely the modified QLBS and RLOP models, from a mathematics perspective which enables RL methods in option pricing through replicating by portfolio. We implement the environment…

Pricing of Securities · Quantitative Finance 2022-05-12 Ziheng Chen

This paper explores the application of a reinforcement learning (RL) framework using the Q-Learning algorithm to enhance dynamic pricing strategies in the retail sector. Unlike traditional pricing methods, which often rely on static demand…

Machine Learning · Computer Science 2024-11-28 Mohit Apte , Ketan Kale , Pranav Datar , Pratiksha Deshmukh

We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to…

Pricing of Securities · Quantitative Finance 2024-06-27 John Ery , Loris Michel

This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…

Analysis of PDEs · Mathematics 2022-03-21 Mikhail V. Klibanov , Kirill V. Golubnichiy , Andrey V. Nikitin

Q-learning is a popular Reinforcement Learning (RL) algorithm which is widely used in practice with function approximation (Mnih et al., 2015). In contrast, existing theoretical results are pessimistic about Q-learning. For example, (Baird,…

Machine Learning · Computer Science 2021-10-20 Naman Agarwal , Syomantak Chaudhuri , Prateek Jain , Dheeraj Nagaraj , Praneeth Netrapalli

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get…

Computational Finance · Quantitative Finance 2009-03-19 Vladimir G. Ivancevic

In recent years, $Q$-learning has become indispensable for model-free reinforcement learning (MFRL). However, it suffers from well-known problems such as under- and overestimation bias of the value, which may adversely affect the policy…

Machine Learning · Computer Science 2021-02-09 Youngmin Oh , Jinwoo Shin , Eunho Yang , Sung Ju Hwang

In this paper, two Q-learning (QL) methods are proposed and their convergence theories are established for addressing the model-free optimal control problem of general nonlinear continuous-time systems. By introducing the Q-function for…

Systems and Control · Computer Science 2014-10-14 Biao Luo , Derong Liu , Tingwen Huang

We extend the QLBS model by reformulating via considering a large trader whose transactions leave a permanent impact on the evolution of the exchange rate process and therefore affect the price of contingent claims on such processes.…

Mathematical Finance · Quantitative Finance 2023-11-14 Ahmet Umur Özsoy , Ömür Uğur

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

In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…

Mathematical Finance · Quantitative Finance 2022-10-12 Michael V. Klibanov , Aleksander A. Shananin , Kirill V. Golubnichiy , Sergey M. Kravchenko

Reinforcement learning (RL) has seen significant research and application results but often requires large amounts of training data. This paper proposes two data-efficient off-policy RL methods that use parametrized Q-learning. In these…

Systems and Control · Electrical Eng. & Systems 2025-04-09 J. S. van Hulst , W. P. M. H. Heemels , D. J. Antunes

Much research has been done to analyze the stock market. After all, if one can determine a pattern in the chaotic frenzy of transactions, then they could make a hefty profit from capitalizing on these insights. As such, the goal of our…

Machine Learning · Computer Science 2025-05-27 Ziyi Zhou , Nicholas Stern , Julien Laasri
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