Konark Jain, Nick Firoozye, Jonathan Kochems, Philip Treleaven
Limit Order Books (LOBs) serve as a mechanism for buyers and sellers to interact with each other in the financial markets. Modelling and simulating LOBs is quite often necessary} for calibrating and fine-tuning the automated trading strategies developed in algorithmic trading research. The recent AI revolution and availability of faster and cheaper compute power has enabled the modelling and simulations to grow richer and even use modern AI techniques. In this review we highlight{examine} the various kinds of LOB simulation models present in the current state of the art. We provide a classification of the models on the basis of their methodology and provide an aggregate view of the popular stylized facts used in the literature to test the models. We additionally provide a focused study of price impact's presence in the models since it is one of the more crucial phenomena to model in algorithmic trading. Finally, we conduct a comparative analysis of various qualities of fits of these models and how they perform when tested against empirical data.
{"title":"Limit Order Book Simulations: A Review","authors":"Konark Jain, Nick Firoozye, Jonathan Kochems, Philip Treleaven","doi":"arxiv-2402.17359","DOIUrl":"https://doi.org/arxiv-2402.17359","url":null,"abstract":"Limit Order Books (LOBs) serve as a mechanism for buyers and sellers to\u0000interact with each other in the financial markets. Modelling and simulating\u0000LOBs is quite often necessary} for calibrating and fine-tuning the automated\u0000trading strategies developed in algorithmic trading research. The recent AI\u0000revolution and availability of faster and cheaper compute power has enabled the\u0000modelling and simulations to grow richer and even use modern AI techniques. In\u0000this review we highlight{examine} the various kinds of LOB simulation models\u0000present in the current state of the art. We provide a classification of the\u0000models on the basis of their methodology and provide an aggregate view of the\u0000popular stylized facts used in the literature to test the models. We\u0000additionally provide a focused study of price impact's presence in the models\u0000since it is one of the more crucial phenomena to model in algorithmic trading.\u0000Finally, we conduct a comparative analysis of various qualities of fits of\u0000these models and how they perform when tested against empirical data.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly operations in the algorithms, one of which is preparing a quantum state that encodes a probability distribution of the underlying asset price. In particular, in pricing a path-dependent option, we need to generate a state encoding a joint distribution of the underlying asset price at multiple time points, which is more demanding. To address these issues, we propose a novel approach using Matrix Product State (MPS) as a generative model for time series generation. To validate our approach, taking the Heston model as a target, we conduct numerical experiments to generate time series in the model. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers.
{"title":"Time series generation for option pricing on quantum computers using tensor network","authors":"Nozomu Kobayashi, Yoshiyuki Suimon, Koichi Miyamoto","doi":"arxiv-2402.17148","DOIUrl":"https://doi.org/arxiv-2402.17148","url":null,"abstract":"Finance, especially option pricing, is a promising industrial field that\u0000might benefit from quantum computing. While quantum algorithms for option\u0000pricing have been proposed, it is desired to devise more efficient\u0000implementations of costly operations in the algorithms, one of which is\u0000preparing a quantum state that encodes a probability distribution of the\u0000underlying asset price. In particular, in pricing a path-dependent option, we\u0000need to generate a state encoding a joint distribution of the underlying asset\u0000price at multiple time points, which is more demanding. To address these\u0000issues, we propose a novel approach using Matrix Product State (MPS) as a\u0000generative model for time series generation. To validate our approach, taking\u0000the Heston model as a target, we conduct numerical experiments to generate time\u0000series in the model. Our findings demonstrate the capability of the MPS model\u0000to generate paths in the Heston model, highlighting its potential for\u0000path-dependent option pricing on quantum computers.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qishuo Cheng, Le Yang, Jiajian Zheng, Miao Tian, Duan Xin
Portfolio management issues have been extensively studied in the field of artificial intelligence in recent years, but existing deep learning-based quantitative trading methods have some areas where they could be improved. First of all, the prediction mode of stocks is singular; often, only one trading expert is trained by a model, and the trading decision is solely based on the prediction results of the model. Secondly, the data source used by the model is relatively simple, and only considers the data of the stock itself, ignoring the impact of the whole market risk on the stock. In this paper, the DQN algorithm is introduced into asset management portfolios in a novel and straightforward way, and the performance greatly exceeds the benchmark, which fully proves the effectiveness of the DRL algorithm in portfolio management. This also inspires us to consider the complexity of financial problems, and the use of algorithms should be fully combined with the problems to adapt. Finally, in this paper, the strategy is implemented by selecting the assets and actions with the largest Q value. Since different assets are trained separately as environments, there may be a phenomenon of Q value drift among different assets (different assets have different Q value distribution areas), which may easily lead to incorrect asset selection. Consider adding constraints so that the Q values of different assets share a Q value distribution to improve results.
{"title":"Optimizing Portfolio Management and Risk Assessment in Digital Assets Using Deep Learning for Predictive Analysis","authors":"Qishuo Cheng, Le Yang, Jiajian Zheng, Miao Tian, Duan Xin","doi":"arxiv-2402.15994","DOIUrl":"https://doi.org/arxiv-2402.15994","url":null,"abstract":"Portfolio management issues have been extensively studied in the field of\u0000artificial intelligence in recent years, but existing deep learning-based\u0000quantitative trading methods have some areas where they could be improved.\u0000First of all, the prediction mode of stocks is singular; often, only one\u0000trading expert is trained by a model, and the trading decision is solely based\u0000on the prediction results of the model. Secondly, the data source used by the\u0000model is relatively simple, and only considers the data of the stock itself,\u0000ignoring the impact of the whole market risk on the stock. In this paper, the\u0000DQN algorithm is introduced into asset management portfolios in a novel and\u0000straightforward way, and the performance greatly exceeds the benchmark, which\u0000fully proves the effectiveness of the DRL algorithm in portfolio management.\u0000This also inspires us to consider the complexity of financial problems, and the\u0000use of algorithms should be fully combined with the problems to adapt. Finally,\u0000in this paper, the strategy is implemented by selecting the assets and actions\u0000with the largest Q value. Since different assets are trained separately as\u0000environments, there may be a phenomenon of Q value drift among different assets\u0000(different assets have different Q value distribution areas), which may easily\u0000lead to incorrect asset selection. Consider adding constraints so that the Q\u0000values of different assets share a Q value distribution to improve results.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139977398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far as we know up to date this simple and probabilistic form of the solution has not appeared in the literature. Next, we apply the general result for the study of the case where the risky asset is given by a fractional Brownian Motion and the information flow of the investor can be diversified.
{"title":"A Note on Optimal Liquidation with Linear Price Impact","authors":"Yan Dolinsky, Doron Greenstein","doi":"arxiv-2402.14100","DOIUrl":"https://doi.org/arxiv-2402.14100","url":null,"abstract":"In this note we consider the maximization of the expected terminal wealth for\u0000the setup of quadratic transaction costs. First, we provide a very simple\u0000probabilistic solution to the problem. Although the problem was largely\u0000studied, as far as we know up to date this simple and probabilistic form of the\u0000solution has not appeared in the literature. Next, we apply the general result\u0000for the study of the case where the risky asset is given by a fractional\u0000Brownian Motion and the information flow of the investor can be diversified.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrei Neagu, Frédéric Godin, Clarence Simard, Leila Kosseim
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 Learning (RL) models were recently proposed to tackle this task. However, existing RL works for hedging do not consider market impact caused by the finite liquidity of traded instruments. Integrating such feature can be crucial to achieve optimal performance when hedging options on stocks with limited liquidity. In this paper, we propose a novel general market impact dynamic hedging model based on Deep Reinforcement Learning (DRL) that considers several realistic features such as convex market impacts, and impact persistence through time. The optimal policy obtained from the DRL model is analysed using several option hedging simulations and compared to commonly used procedures such as delta hedging. Results show our DRL model behaves better in contexts of low liquidity by, among others: 1) learning the extent to which portfolio rebalancing actions should be dampened or delayed to avoid high costs, 2) factoring in the impact of features not considered by conventional approaches, such as previous hedging errors through the portfolio value, and the underlying asset's drift (i.e. the magnitude of its expected return).
{"title":"Deep Hedging with Market Impact","authors":"Andrei Neagu, Frédéric Godin, Clarence Simard, Leila Kosseim","doi":"arxiv-2402.13326","DOIUrl":"https://doi.org/arxiv-2402.13326","url":null,"abstract":"Dynamic hedging is the practice of periodically transacting financial\u0000instruments to offset the risk caused by an investment or a liability. Dynamic\u0000hedging optimization can be framed as a sequential decision problem; thus,\u0000Reinforcement Learning (RL) models were recently proposed to tackle this task.\u0000However, existing RL works for hedging do not consider market impact caused by\u0000the finite liquidity of traded instruments. Integrating such feature can be\u0000crucial to achieve optimal performance when hedging options on stocks with\u0000limited liquidity. In this paper, we propose a novel general market impact\u0000dynamic hedging model based on Deep Reinforcement Learning (DRL) that considers\u0000several realistic features such as convex market impacts, and impact\u0000persistence through time. The optimal policy obtained from the DRL model is\u0000analysed using several option hedging simulations and compared to commonly used\u0000procedures such as delta hedging. Results show our DRL model behaves better in\u0000contexts of low liquidity by, among others: 1) learning the extent to which\u0000portfolio rebalancing actions should be dampened or delayed to avoid high\u0000costs, 2) factoring in the impact of features not considered by conventional\u0000approaches, such as previous hedging errors through the portfolio value, and\u0000the underlying asset's drift (i.e. the magnitude of its expected return).","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"282 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139925390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Johann Lussange, Stefano Vrizzi, Stefano Palminteri, Boris Gutkin
Building on a previous foundation work (Lussange et al. 2020), this study introduces a multi-agent reinforcement learning (MARL) model simulating crypto markets, which is calibrated to the Binance's daily closing prices of $153$ cryptocurrencies that were continuously traded between 2018 and 2022. Unlike previous agent-based models (ABM) or multi-agent systems (MAS) which relied on zero-intelligence agents or single autonomous agent methodologies, our approach relies on endowing agents with reinforcement learning (RL) techniques in order to model crypto markets. This integration is designed to emulate, with a bottom-up approach to complexity inference, both individual and collective agents, ensuring robustness in the recent volatile conditions of such markets and during the COVID-19 era. A key feature of our model also lies in the fact that its autonomous agents perform asset price valuation based on two sources of information: the market prices themselves, and the approximation of the crypto assets fundamental values beyond what those market prices are. Our MAS calibration against real market data allows for an accurate emulation of crypto markets microstructure and probing key market behaviors, in both the bearish and bullish regimes of that particular time period.
{"title":"Modelling crypto markets by multi-agent reinforcement learning","authors":"Johann Lussange, Stefano Vrizzi, Stefano Palminteri, Boris Gutkin","doi":"arxiv-2402.10803","DOIUrl":"https://doi.org/arxiv-2402.10803","url":null,"abstract":"Building on a previous foundation work (Lussange et al. 2020), this study\u0000introduces a multi-agent reinforcement learning (MARL) model simulating crypto\u0000markets, which is calibrated to the Binance's daily closing prices of $153$\u0000cryptocurrencies that were continuously traded between 2018 and 2022. Unlike\u0000previous agent-based models (ABM) or multi-agent systems (MAS) which relied on\u0000zero-intelligence agents or single autonomous agent methodologies, our approach\u0000relies on endowing agents with reinforcement learning (RL) techniques in order\u0000to model crypto markets. This integration is designed to emulate, with a\u0000bottom-up approach to complexity inference, both individual and collective\u0000agents, ensuring robustness in the recent volatile conditions of such markets\u0000and during the COVID-19 era. A key feature of our model also lies in the fact\u0000that its autonomous agents perform asset price valuation based on two sources\u0000of information: the market prices themselves, and the approximation of the\u0000crypto assets fundamental values beyond what those market prices are. Our MAS\u0000calibration against real market data allows for an accurate emulation of crypto\u0000markets microstructure and probing key market behaviors, in both the bearish\u0000and bullish regimes of that particular time period.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, we introduced a new paradigm for alpha mining in the realm of quantitative investment, developing a new interactive alpha mining system framework, Alpha-GPT. This system is centered on iterative Human-AI interaction based on large language models, introducing a Human-in-the-Loop approach to alpha discovery. In this paper, we present the next-generation Alpha-GPT 2.0 footnote{Draft. Work in progress}, a quantitative investment framework that further encompasses crucial modeling and analysis phases in quantitative investment. This framework emphasizes the iterative, interactive research between humans and AI, embodying a Human-in-the-Loop strategy throughout the entire quantitative investment pipeline. By assimilating the insights of human researchers into the systematic alpha research process, we effectively leverage the Human-in-the-Loop approach, enhancing the efficiency and precision of quantitative investment research.
{"title":"Alpha-GPT 2.0: Human-in-the-Loop AI for Quantitative Investment","authors":"Hang Yuan, Saizhuo Wang, Jian Guo","doi":"arxiv-2402.09746","DOIUrl":"https://doi.org/arxiv-2402.09746","url":null,"abstract":"Recently, we introduced a new paradigm for alpha mining in the realm of\u0000quantitative investment, developing a new interactive alpha mining system\u0000framework, Alpha-GPT. This system is centered on iterative Human-AI interaction\u0000based on large language models, introducing a Human-in-the-Loop approach to\u0000alpha discovery. In this paper, we present the next-generation Alpha-GPT 2.0\u0000footnote{Draft. Work in progress}, a quantitative investment framework that\u0000further encompasses crucial modeling and analysis phases in quantitative\u0000investment. This framework emphasizes the iterative, interactive research\u0000between humans and AI, embodying a Human-in-the-Loop strategy throughout the\u0000entire quantitative investment pipeline. By assimilating the insights of human\u0000researchers into the systematic alpha research process, we effectively leverage\u0000the Human-in-the-Loop approach, enhancing the efficiency and precision of\u0000quantitative investment research.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"80 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139753439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The formulaic alphas are mathematical formulas that transform raw stock data into indicated signals. In the industry, a collection of formulaic alphas is combined to enhance modeling accuracy. Existing alpha mining only employs the neural network agent, unable to utilize the structural information of the solution space. Moreover, they didn't consider the correlation between alphas in the collection, which limits the synergistic performance. To address these problems, we propose a novel alpha mining framework, which formulates the alpha mining problems as a reward-dense Markov Decision Process (MDP) and solves the MDP by the risk-seeking Monte Carlo Tree Search (MCTS). The MCTS-based agent fully exploits the structural information of discrete solution space and the risk-seeking policy explicitly optimizes the best-case performance rather than average outcomes. Comprehensive experiments are conducted to demonstrate the efficiency of our framework. Our method outperforms all state-of-the-art benchmarks on two real-world stock sets under various metrics. Backtest experiments show that our alphas achieve the most profitable results under a realistic trading setting.
{"title":"RiskMiner: Discovering Formulaic Alphas via Risk Seeking Monte Carlo Tree Search","authors":"Tao Ren, Ruihan Zhou, Jinyang Jiang, Jiafeng Liang, Qinghao Wang, Yijie Peng","doi":"arxiv-2402.07080","DOIUrl":"https://doi.org/arxiv-2402.07080","url":null,"abstract":"The formulaic alphas are mathematical formulas that transform raw stock data\u0000into indicated signals. In the industry, a collection of formulaic alphas is\u0000combined to enhance modeling accuracy. Existing alpha mining only employs the\u0000neural network agent, unable to utilize the structural information of the\u0000solution space. Moreover, they didn't consider the correlation between alphas\u0000in the collection, which limits the synergistic performance. To address these\u0000problems, we propose a novel alpha mining framework, which formulates the alpha\u0000mining problems as a reward-dense Markov Decision Process (MDP) and solves the\u0000MDP by the risk-seeking Monte Carlo Tree Search (MCTS). The MCTS-based agent\u0000fully exploits the structural information of discrete solution space and the\u0000risk-seeking policy explicitly optimizes the best-case performance rather than\u0000average outcomes. Comprehensive experiments are conducted to demonstrate the\u0000efficiency of our framework. Our method outperforms all state-of-the-art\u0000benchmarks on two real-world stock sets under various metrics. Backtest\u0000experiments show that our alphas achieve the most profitable results under a\u0000realistic trading setting.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139753426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Prices of option contracts on two assets within uncertain volatility models for worst and best-case scenarios satisfy a two-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with cross derivatives terms. Traditional methods mainly involve finite differences and policy iteration. This "discretize, then optimize" paradigm requires complex rotations of computational stencils for monotonicity. This paper presents a novel and more streamlined "decompose and integrate, then optimize" approach to tackle the aforementioned HJB PDE. Within each timestep, our strategy employs a piecewise constant control, breaking down the HJB PDE into independent linear two-dimensional PDEs. Using known closed-form expressions for the Fourier transforms of the Green's functions associated with these PDEs, we determine an explicit formula for these functions. Since the Green's functions are non-negative, the solutions to the PDEs, cast as two-dimensional convolution integrals, can be conveniently approximated using a monotone integration method. Such integration methods, including a composite quadrature rule, are generally available in popular programming languages. To further enhance efficiency, we propose an implementation of this monotone integration scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix structure. Optimal control is subsequently obtained by efficiently synthesizing the solutions of the individual PDEs. The proposed monotone piecewise constant control method is demonstrated to be both $ell_{infty} $-stable and consistent in the viscosity sense, ensuring its convergence to the viscosity solution of the HJB equation. Numerical results show remarkable agreement with benchmark solutions obtained by unconditionally monotone finite differences, tree methods, and Monte Carlo simulation, underscoring the robustness and effectiveness of our method.
{"title":"A monotone piecewise constant control integration approach for the two-factor uncertain volatility model","authors":"Duy-Minh Dang, Hao Zhou","doi":"arxiv-2402.06840","DOIUrl":"https://doi.org/arxiv-2402.06840","url":null,"abstract":"Prices of option contracts on two assets within uncertain volatility models\u0000for worst and best-case scenarios satisfy a two-dimensional\u0000Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with cross\u0000derivatives terms. Traditional methods mainly involve finite differences and\u0000policy iteration. This \"discretize, then optimize\" paradigm requires complex\u0000rotations of computational stencils for monotonicity. This paper presents a novel and more streamlined \"decompose and integrate,\u0000then optimize\" approach to tackle the aforementioned HJB PDE. Within each\u0000timestep, our strategy employs a piecewise constant control, breaking down the\u0000HJB PDE into independent linear two-dimensional PDEs. Using known closed-form\u0000expressions for the Fourier transforms of the Green's functions associated with\u0000these PDEs, we determine an explicit formula for these functions. Since the\u0000Green's functions are non-negative, the solutions to the PDEs, cast as\u0000two-dimensional convolution integrals, can be conveniently approximated using a\u0000monotone integration method. Such integration methods, including a composite\u0000quadrature rule, are generally available in popular programming languages. To\u0000further enhance efficiency, we propose an implementation of this monotone\u0000integration scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix\u0000structure. Optimal control is subsequently obtained by efficiently synthesizing\u0000the solutions of the individual PDEs. The proposed monotone piecewise constant control method is demonstrated to be\u0000both $ell_{infty} $-stable and consistent in the viscosity sense, ensuring\u0000its convergence to the viscosity solution of the HJB equation. Numerical\u0000results show remarkable agreement with benchmark solutions obtained by\u0000unconditionally monotone finite differences, tree methods, and Monte Carlo\u0000simulation, underscoring the robustness and effectiveness of our method.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139753437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Autonomous agents based on Large Language Models (LLMs) that devise plans and tackle real-world challenges have gained prominence.However, tailoring these agents for specialized domains like quantitative investment remains a formidable task. The core challenge involves efficiently building and integrating a domain-specific knowledge base for the agent's learning process. This paper introduces a principled framework to address this challenge, comprising a two-layer loop.In the inner loop, the agent refines its responses by drawing from its knowledge base, while in the outer loop, these responses are tested in real-world scenarios to automatically enhance the knowledge base with new insights.We demonstrate that our approach enables the agent to progressively approximate optimal behavior with provable efficiency.Furthermore, we instantiate this framework through an autonomous agent for mining trading signals named QuantAgent. Empirical results showcase QuantAgent's capability in uncovering viable financial signals and enhancing the accuracy of financial forecasts.
{"title":"QuantAgent: Seeking Holy Grail in Trading by Self-Improving Large Language Model","authors":"Saizhuo Wang, Hang Yuan, Lionel M. Ni, Jian Guo","doi":"arxiv-2402.03755","DOIUrl":"https://doi.org/arxiv-2402.03755","url":null,"abstract":"Autonomous agents based on Large Language Models (LLMs) that devise plans and\u0000tackle real-world challenges have gained prominence.However, tailoring these\u0000agents for specialized domains like quantitative investment remains a\u0000formidable task. The core challenge involves efficiently building and\u0000integrating a domain-specific knowledge base for the agent's learning process.\u0000This paper introduces a principled framework to address this challenge,\u0000comprising a two-layer loop.In the inner loop, the agent refines its responses\u0000by drawing from its knowledge base, while in the outer loop, these responses\u0000are tested in real-world scenarios to automatically enhance the knowledge base\u0000with new insights.We demonstrate that our approach enables the agent to\u0000progressively approximate optimal behavior with provable\u0000efficiency.Furthermore, we instantiate this framework through an autonomous\u0000agent for mining trading signals named QuantAgent. Empirical results showcase\u0000QuantAgent's capability in uncovering viable financial signals and enhancing\u0000the accuracy of financial forecasts.","PeriodicalId":501294,"journal":{"name":"arXiv - QuantFin - Computational Finance","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139753436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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