We find the explicit expression for the equilibrium wealth distribution of the Directed Random Market process, recently introduced by Martínez-Martínez and López-Ruiz, which turns out to be a Gamma distribution with shape parameter . We also prove the convergence of the discrete-time process describing the…
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48 results for “equilibrium distribution”
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the…
We consider a financial market model which consists of a financial asset and a large number of interacting agents classified into many types. Different types of agents are heterogeneous in their price expectations. Each agent can change its type based on the current empirical distribution of the types and the equilibri…
The paper introduces Robust Correlated Equilibrium for games with time-varying costs and proposes an algorithm to achieve it.
problem Games with time-varying costs and disturbances.
method Proposes Robust Correlated Equilibrium and a decentralized algorithm to learn optimal strategies.
result The algorithm converges to the Robust Correlated Equilibrium, showing no regret for each controller.
On the generalization ability of coarse-grained molecular dynamics models for non-equilibrium processesphysics.comp-ph
New CGMD model predicts non-equilibrium processes better than existing methods.
problem Inconsistency in conditional distribution of unresolved variables.
method Time-lagged independent component analysis to minimize entropy contribution of unresolved variables.
result The model's generalization ability for non-equilibrium processes is significantly improved.
Gradient equilibrium improves online learning performance without requiring sublinear regret.
problem Achieving sublinear regret in online learning.
method Gradient equilibrium: average of gradients converges to zero.
result Gradient equilibrium can be achieved by standard online learning methods.
The paper characterizes equilibrium strategies under random risk aversion, showing unique solutions based on risk aversion distribution.
problem Characterizing equilibrium strategies in a continuous-time portfolio selection problem under random risk aversion.
method Provided a complete characterization of all deterministic equilibrium strategies in closed form, analyzing the structure of the solution based on the distribution of random risk aversion.
result The equilibrium is unique (if exists) when the expectation of random risk aversion is finite, but infinite expectation leads to either infinitely many equilibria or a unique trivial one.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernelsstat.ML
Paper studies t-SNE convergence with generalized kernels.
problem Understanding convergence of t-SNE with generalized kernels.
method Concrete formulation of generalized kernels, proving convergence to an equilibrium distribution.
result t-SNE converges to an equilibrium distribution under certain conditions for generalized kernels.
Informed trading, limit order book and implementation shortfall: equilibrium and asymptoticsq-fin.TR
Modeling trading behavior with information signals and limit order books, showing market impact and equilibrium properties.
problem Analyzing the impact of information signals on trading behavior and market equilibrium in limit order books.
method Static equilibrium model with profit-maximizing investors and competitive dealers, using iterative algorithms and asymptotic analysis.
result The market impact of large trades follows a power law with fat tails and a logarithmic law with lighter tails, and the order book flattens as noise trading increases.
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity …
Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimenstional typesq-fin.TR
We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplie…
Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational effort is invested for simulating these system in small steps, e.g., using Molecular…
DDEQs extend DEQs to discrete measure inputs using Wasserstein gradient flows.
problem Applying DEQs to discrete measure inputs like sets or point clouds.
method Wasserstein gradient flows for finding fixed points of discrete measures under permutation-invariance.
result DDEQs can compete with state-of-the-art models in tasks like point cloud classification and completion.
General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will p…
In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an -dimensional multi-agent economic system implies the exponential (Boltzmann-Gibss) wealth distribution an…
Kinetic theory models for the distribution of wealth: power law from overlap of exponentialsphysics.soc-ph
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions, and their equivalence to the Ma…
We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the …
Equilibrium master equations for time-inconsistent problems with distribution dependent rewardsq-fin.MF
Unified approach to time-inconsistent problems with distribution-dependent rewards.
problem Time-inconsistent problems with distribution-dependent rewards in behavioral finance and economics.
method Equilibrium master equation on Wasserstein space, refined derivatives, Itô's formula.
result Unified approach to find equilibrium solutions for time-inconsistent problems.
The statistical distribution of money and the rate of money transferencecond-mat.stat-mech
The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma function, confirming the validity of the statistical distribution at equilibriu…
We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-bala…
We consider a simple stochastic model of a urban rental housing market, in which the interaction of tenants and landlords induces rent fluctuations. We simulate the model numerically and measure the equilibrium rent distribution, which is found to be close to a lognormal law. We also study the influence of the density …
Economic systems are similar with physic systems for their large number of individuals and the exist of equilibrium. In this paper, we present a model applying the equilibrium statistical model in economic systems. Consistent with statistical physics, we define a series of concepts, such as economic temperature, econom…
Agents prefer non-diversification in markets with extreme losses.
problem Optimal risk allocation and equilibria in markets with extremely heavy-tailed losses.
method Analysis of super-Pareto loss distributions and stochastic dominance.
result Non-diversification is preferred in markets with super-Pareto losses.
We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is a…
Improved sampling for gauge theory with SNFs.
problem Sampling from target probability distributions in gauge theory.
method Stochastic Normalizing Flows (SNFs) for lattice gauge theory.
result Promising scaling properties of SNFs with degrees of freedom.
Path-independent equilibrium models improve network performance on harder problems.
problem Improving network performance on harder problem instances.
method Investigated path-independent equilibrium models and their impact on network performance.
result Path independence correlates with better performance on harder problem instances.
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
Study compares cryptocurrency and stock markets using statistical equilibrium models.
problem Comparing the stochastic structure of cryptocurrency and stock markets.
method Applied QRSE model to analyze daily returns of cryptocurrencies and S&P 500 companies.
result Revealed differences in informational efficiency between cryptocurrency and stock markets.
New algorithm converges to equilibrium in nonconvex-nonconcave optimization problems without dimension dependence.
problem Min-max optimization in nonconvex-nonconcave landscapes.
method Convergent algorithm with greedy max-player updates and proposal distribution for min-player.
result Algorithm converges to equilibrium in non-dependent iterations, suitable for GAN training.
We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established eq…
We derive asset pricing formula for markets with incomplete information and subjective views.
problem Asset pricing in markets with informational imperfections and subjective investor beliefs.
method Closed-form market equilibrium formula based on Merton's model, non-linear system of equations, conditional posterior distribution.
result Derivation of market reference model for excess returns under random shadow-costs.
Evolution of the distribution of wealth in an economic environment driven by local Nash equilibriaq-fin.GN
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents i…
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related…
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for -mixed Nash equilibrium.
Equilibrium singular dividend control under ambiguity aggregation of heterogeneous discount ratesmath.OC
A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.
problem Optimizing dividends for a firm with heterogeneous shareholders under ambiguity aggregation.
method Characterizing equilibrium dividends using a partition of the state space.
result Time-homogeneous equilibrium dividend law characterized by a partition of the state space.
Productivity and credit limits affect aggregate production in non-monotonic ways.
problem Understanding how aggregate production is influenced by individual characteristics and financial constraints.
method Analytical proof of non-monotonic effects of productivity and credit limits on aggregate production in a general equilibrium model.
result Equilibrium aggregate production can be non-monotonic in both individual productivity and credit limit.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
This paper studies how relative performance concerns affect stock prices in a tree-like market model.
problem The impact of relative performance concerns on stock prices in a tree-like market model.
method Mean-field equilibrium analysis in a binomial tree framework with exponential utility.
result Existence and uniqueness of market-clearing mean-field equilibrium in both single- and multi-population settings.
Self-Financing, Replicating Hedging Strategies, an incomplete thermodynamic analogycond-mat.stat-mech
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge and the option pricing partial differential equation. Approximately reversible tr…
Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.
problem Finding Lagrange multipliers for Maximum-Entropy distributions is computationally challenging.
method Employed Gaussian processes to approximate the Lagrange multipliers as a map of moments. Optimized hyperparameters by maximizing log-likelihood.
result Data-driven Maximum-Entropy closure performs well in approximating non-equilibrium distributions.
Paper proves convergence of Gini index to equilibrium in Wasserstein distance.
problem Proving convergence of Gini index to equilibrium in Wasserstein distance.
method Analyzes Gini index as Lyapunov functional and proves convergence in Wasserstein distance.
result Proves convergence of Gini index to equilibrium in Wasserstein distance.
Micro-Macro Relation of Production - The Double Scaling Law for Statistical Physics of Economy -q-fin.GN
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…
Study of entropy-regularized LQG MFGs with exploratory actions.
problem Optimizing multi-population mean field games with entropy regularization.
method Introduced exploratory actions and derived optimal action distributions.
result Optimal action distributions lead to ε-Nash equilibria in finite-population MFGs.
This paper examines how adversarial perturbations affect model performance and equilibrium learning.
problem Adversarial perturbations and covariate shifts impact model performance and equilibrium learning.
method Characterizes the extrapolation region in regression and classification, analyzes dynamics of adversarial learning games.
result Establishes two directional convergence results: a blessing in regression and a curse in classification.
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the analysis of time-homogeneous equilibria using tools from the theory of one-dimensi…
Develops a method for non-equilibrium importance sampling to estimate expectations and constants.
problem Estimating expectations and normalization constants for complex high-dimensional distributions.
method Generates samples from a base distribution, transports them using a velocity field, and averages along flowlines.
result The method can achieve zero-variance estimation and significantly reduces variance compared to vanilla estimators.