Related papers: From Disequilibrium Markets to Equilibrium
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
Using techniques from information geometry, we construct a semi-Hamiltonian system modelling trader beliefs in a binary asset market and study the impact of inequality or asymmetry in beliefs, information, and power on price dynamics. We…
We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our…
Market equilibrium is one of the most fundamental solution concepts in economics and social optimization analysis. Existing works on market equilibrium computation primarily focus on settings with relatively few buyers. Motivated by this,…
We study the continuous time Kyle-Back model with a risk averse informed trader.We show that in a market with multiple assets and non-Gaussian prices an equilibrium exists. The equilibrium is constructed by considering a Fokker-Planck…
We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk…
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…
The Nikolaevskiy equation has been proposed as a model for seismic waves, electroconvection and weak turbulence; we show that it can also be used to model transverse instabilities of fronts. This equation possesses a large-scale "Goldstone"…
Criticality in the class of disordered systems comprising the random-field Ising model (RFIM) and elastic manifolds in a random environment is controlled by zero-temperature fixed points that must be treated through a functional…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X.\ Guardiola, {\it et. al.}, Phys. Rev E {\bf 66}, 026121 (2002)]. We show that the model…
We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market…
We investigate the asymptotic behaviour of a reduced {\alpha}{\Omega}-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the {\alpha}-effect results in a system with state-dependent stochastic perturbations.…
This contribution aims at presenting and generalizing a recent work of Hernandez, Jara and Valentim [DOI:10.1016/j.spa.2016.06.026]. We consider the weakly asymmetric version of the so-called discrete Atlas model, which has been introduced…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused…
We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences…
In two-stage electricity markets, renewable power producers enter the day-ahead market with a forecast of future power generation and then reconcile any forecast deviation in the real-time market at a penalty. The choice of the forecast…