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We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

Analysis of PDEs · Mathematics 2025-12-22 Michele Coti Zelati , Lucas Ertzbischoff , David Gerard-Varet

We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $\lambda$. We focus on the equilibrium or…

Statistical Mechanics · Physics 2009-11-10 Marco Patriarca , Anirban Chakraborti , Kimmo Kaski

We propose a generalized market equilibrium model using assignment game criteria for evaluating transportation systems that consist of both operators' and users' decisions. The model finds stable pricing, in terms of generalized costs, and…

Computational Engineering, Finance, and Science · Computer Science 2020-08-14 Saeid Rasulkhani , Joseph Y. J. Chow

The existence of a (partial) market equilibrium price is proved in a complete, continuous time finite-agent market setting. The economic agents act as price takers in a fully competitive setting and maximize exponential utility from…

Mathematical Finance · Quantitative Finance 2022-12-01 Alessandro Prosperi

We describe a new model to simulate the dynamic interactions between market price and the decisions of two different kind of traders. They possess spatial mobility allowing to group together to form coalitions. Each coalition follows a…

Statistical Mechanics · Physics 2009-10-31 Filippo Castiglione

In feature-based dynamic pricing, a seller sets appropriate prices for a sequence of products (described by feature vectors) on the fly by learning from the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$ price, and…

Machine Learning · Computer Science 2022-04-04 Jianyu Xu , Yu-Xiang Wang

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the…

Pricing of Securities · Quantitative Finance 2016-11-28 Jean-Philippe Aguilar , Cyril Coste , Hagen Kleinert , Jan Korbel

We consider sequential search by an agent who cannot observe the quality of goods but can acquire information by buying signals from a profit-maximizing principal with limited commitment power. The principal can charge higher prices for…

Theoretical Economics · Economics 2024-08-13 Teddy Mekonnen , Zeky Murra-Anton , Bobak Pakzad-Hurson

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in…

Mathematical Finance · Quantitative Finance 2016-08-30 Dmitry Kramkov , Sergio Pulido

We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…

Statistical Mechanics · Physics 2008-12-02 D. Sornette , D. Stauffer , H. Takayasu

This paper studies a Kyle-Back model with a risk-averse insider possessing exponential utility and a dynamic stochastic signal about the asset's terminal fundamental value. While the existing literature considers either risk-neutral…

Mathematical Finance · Quantitative Finance 2025-12-05 Albina Danilova , Valentin Lizhdvoy

The "Money Exchange Model" is a type of agent-based simulation model used to study how wealth distribution and inequality evolve through monetary exchanges between individuals. The primary focus of this model is to identify the limiting…

Probability · Mathematics 2025-01-07 Hironobu Sakagawa

Kyle model in continuous time where the insider may be subject to legal penalties is considered. In equilibrium the insider internalises this legal risk by trading less aggressively. The equilibrium is characterised via the solution of a…

Probability · Mathematics 2023-11-22 Umut Çetin

We consider the efficient outcome of a canonical economic market model involving buyers and sellers with independent and identically distributed random valuations and costs, respectively. When the number of buyers and sellers is large, we…

Probability · Mathematics 2017-03-02 Ellen V. Muir , Konstantin Borovkov

We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a…

Analysis of PDEs · Mathematics 2022-07-13 Yves Achdou , Guillaume Carlier , Quentin Petit , Daniela Tonon

We study price discovery in a model where an informed agent has arbitrary private information about state probabilities and trades state-contingent claims. The model unifies the key elements of Arrow-Debreu (1954) and Kyle (1985). When the…

General Economics · Economics 2026-03-23 Christian Keller , Michael C. Tseng

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…

Analysis of PDEs · Mathematics 2020-03-09 Christian Hamster , Hermen Jan Hupkes

This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer…

Trading and Market Microstructure · Quantitative Finance 2015-09-09 Jin Hyuk Choi , Kasper Larsen , Duane J. Seppi

We develop a multi-period Kyle-type model that incorporates both mandatory disclosure of informed trades and imperfect competition among market makers. We prove the existence and uniqueness of a linear equilibrium and show that the…

Trading and Market Microstructure · Quantitative Finance 2026-04-14 Seongjin Kim , Jin Hyuk Choi

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium…

Physics and Society · Physics 2009-07-16 Ignacio Gallo
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