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In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…

Analysis of PDEs · Mathematics 2020-03-05 Diogo Gomes , Julian Gutierrez , Ricardo Ribeiro

Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min-max characterization of the optimal control and price…

Optimization and Control · Mathematics 2023-01-26 Diogo Gomes , Julián Gutiérrez , Mathieu Laurière

We consider the mean-field game price formation model introduced by Gomes and Sa\'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and…

Numerical Analysis · Mathematics 2022-04-05 Yuri Ashrafyan , Tigran Bakaryan , Diogo Gomes , Julian Gutierrez

We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading…

Analysis of PDEs · Mathematics 2022-08-15 Diogo Gomes , Julian Gutierrez , Ricardo Ribeiro

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…

Mathematical Finance · Quantitative Finance 2021-09-28 Masaaki Fujii , Akihiko Takahashi

We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…

Optimization and Control · Mathematics 2024-10-30 Fabio Camilli , Mathieu Laurière , Qing Tang

Ensemble learning is characterized by flexibility, high precision, and refined structure. As a critical component within computational finance, option pricing with machine learning requires both high predictive accuracy and reduced…

Machine Learning · Computer Science 2025-06-09 Zeyuan Li , Qingdao Huang

Data analytics using machine learning (ML) has become ubiquitous in science, business intelligence, journalism and many other domains. While a lot of work focuses on reducing the training cost, inference runtime and storage cost of ML…

Databases · Computer Science 2018-05-30 Lingjiao Chen , Paraschos Koutris , Arun Kumar

The problem of market clearing is to set a price for an item such that quantity demanded equals quantity supplied. In this work, we cast the problem of predicting clearing prices into a learning framework and use the resulting models to…

Machine Learning · Computer Science 2019-06-25 Weiran Shen , Sébastien Lahaie , Renato Paes Leme

We propose two novel frameworks to study the price formation of an asset negotiated in an order book. Specifically, we develop a game-theoretic model in many-person games and mean-field games, considering costs stemming from limited…

Trading and Market Microstructure · Quantitative Finance 2022-02-24 David Evangelista , Yuri Saporito , Yuri Thamsten

This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross \& Rubinstein. For agents with exponential and…

Mathematical Finance · Quantitative Finance 2025-12-23 Masaaki Fujii

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin

In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…

Optimization and Control · Mathematics 2019-07-24 Dena Firoozi , Peter E. Caines , Sebastian Jaimungal

A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price…

Statistical Mechanics · Physics 2008-12-02 J. Doyne Farmer , Shareen Joshi

We consider a mean-field game model where the cost functions depend on a fixed parameter, called \textit{state}, which is unknown to players. Players learn about the state from a a stream of private signals they receive throughout the game.…

Optimization and Control · Mathematics 2024-02-01 Eran Shmaya , Bruno Ziliotto

We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual…

Optimization and Control · Mathematics 2025-09-18 Xu Wang , Samy Wu Fung , Levon Nurbekyan

We consider the problem of dynamic pricing of a product in the presence of feature-dependent price sensitivity. Developing practical algorithms that can estimate price elasticities robustly, especially when information about no purchases…

Machine Learning · Statistics 2022-12-21 Ravi Kumar , Shahin Boluki , Karl Isler , Jonas Rauch , Darius Walczak

We consider a scenario where a seller possesses a dataset $D$ and trains it into models of varying accuracies for sale in the market. Due to the reproducibility of data, the dataset can be reused to train models with different accuracies,…

Artificial Intelligence · Computer Science 2025-04-01 Jie Liu , Tao Feng , Yan Jiang , Peizheng Wang , Chao Wu

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been…

Mathematical Finance · Quantitative Finance 2024-11-13 Masaaki Fujii , Masashi Sekine

In the context of advertising auctions, finding good reserve prices is a notoriously challenging learning problem. This is due to the heterogeneity of ad opportunity types and the non-convexity of the objective function. In this work, we…

Machine Learning · Computer Science 2017-11-07 Andrés Muñoz Medina , Sergei Vassilvitskii
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