Two-cycle GEILA equilibria are OLG equilibria and vice versa, with applications to indeterminacy and bubbles.
problem Relationship between GEILA and OLG models.
method Proof of equilibrium equivalence and application to indeterminacy and bubbles.
result GEILA and OLG models are equivalent under certain conditions.
We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity.…
A new method relaxes molecules without needing non-equilibrium data.
problem Molecular relaxation requires understanding non-equilibrium structures.
method MoreRed: molecular relaxation by reverse diffusion with time step prediction.
result MoreRed learns a simpler pseudo potential energy surface.
Existence of Radner equilibrium proven with growing population.
problem Analyzing Radner equilibrium in a model with population growth.
method Proved existence of equilibrium for growing population using mathematical analysis.
result Equilibrium exists for a growing population, with effects on annuity prices.
DEQs converge to optimal solutions with mild over-parameterization.
problem Training over-parameterized deep equilibrium models.
method Solves equilibrium point directly, uses gradient descent, and analyzes convergence via linear rate.
result Gradient descent converges to a globally optimal solution at a linear rate for quadratic loss.
Kyle's equilibrium model stability proven for 1-2 trading times, but not for 3 or more.
problem Stability of Kyle's equilibrium model in a dynamic trading setting.
method Proof of stability for 1-2 trading times, non-stability for 3 or more trading times, independent of input parameters.
result Kyle's equilibrium model is stable for 1-2 trading times but not for 3 or more trading times.
We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an a…
Existence of incomplete Radner equilibrium with endogenous noise tracker.
problem Existence of incomplete Radner equilibrium in a model with endogenous noise tracker.
method Proved existence through a coupled system of ODEs, reduced to two coupled ODEs.
result Endogenous noise tracker leads to higher aggregate welfare for large stock supply.
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
The theorems we proved describe the structure of economic equilibrium in the exchange economy model. We have studied the structure of property vectors under given structure of demand vectors at which given price vector is equilibrium one. On this ground, we describe the general structure of the equilibrium state and gi…
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.
Market equilibrium price proven in a large-agent model.
problem Proving market equilibrium in a large-agent setting.
method Proved existence of equilibrium price in a complete, continuous time market with infinite agents.
result The equilibrium price dynamics decouple as the number of agents 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 …
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
Geometric programming approach for traffic equilibrium problems.
problem Optimizing traffic equilibrium in transportation systems.
method Finslerian dynamical model for nonlinear complementarity problems.
result Effective solution for various equilibrium problems in transportation.
Develops asset pricing models with mean field game theory for heterogeneous agents.
problem Tackles equilibrium asset pricing in incomplete markets with heterogeneous agents.
method Uses mean field game theory and mean field backward stochastic differential equations (BSDEs).
result Derives equilibrium risk premium and shows market clearing in the large population limit.
RevDEQs improve performance on tasks with exact gradients and fewer function evaluations.
problem Inexact gradient calculation in DEQs leads to unstable training and requires regularisation or many function evaluations.
method Introduce Reversible Deep Equilibrium Models (RevDEQs) that allow for exact gradient calculation, no regularisation, and far fewer function evaluations.
result RevDEQs significantly improve performance on language modelling and image classification tasks.
Investigates price dynamics of two assets with and without bubbles, deriving conditions for equilibrium prices.
problem Understanding price dynamics and bubbles in multi-asset markets.
method Derives sufficient and necessary conditions for average equilibrium price dynamics in a two-asset model.
result Assets with positive average dividends display hump-shaped bubbles, while those with constant fundamental values show misvaluation effects.
This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that the disagreement about nullsets naturally leads to equilibrium asset pricing bubb…
Study equilibrium consumption habits in a large population using mean field games.
problem Equilibrium consumption under external habit formation in a large population.
method Formulated and solved mean field games for linear and multiplicative habit formation preferences, constructed approximate Nash equilibria for large n-player games.
result Characterized mean field equilibrium strategies and derived financial implications.
Proves existence of equilibrium in limited participation economy.
problem Existence of an equilibrium in an economy with limited financial market access.
method Proves global existence of Radner equilibrium using BSDEs with unique solution.
result Proves existence of Radner equilibrium with limited participation.
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [y], inflation [π] and nominal interest rate [$…
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
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.
Paper analyzes strategic underreporting in competitive insurance markets.
problem Strategic underreporting by insureds in competitive insurance markets.
method Develops a dynamic insurance market model with two competing companies and a continuum of insureds, examines the interaction between strategic underreporting and competitive pricing under a Bonus-Malus System framework.
result Establishes the existence and uniqueness of the insureds' optimal reporting barrier and its dependence on BMS premiums; proves the existence of Nash equilibrium premium strategies.
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium…
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…
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed N-player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior. result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.
In this paper, we propose an equilibrium pricing model in a dynamic multi-period stochastic framework with uncertain income streams. In an incomplete market, there exist two traded risky assets (e.g. stock/commodity and weather derivative) and a non-traded underlying (e.g. temperature). The risk preferences are of expo…
In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …
We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of p…
Dynamic pricing model considers ambiguity in endowment growth rate.
problem Dynamic asset pricing under ambiguous endowment growth rate.
method α-maxmin expected utility model for ambiguity, intra-personal equilibrium strategies, market equilibrium.
result Asset prices reflect ambiguity in endowment growth rate.
The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique an…
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.
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.
Study proves existence and convergence of discrete-time Kyle models with multiple insiders.
problem Existence and convergence of discrete-time Kyle models with multiple informed traders.
method Proves existence and convergence of discrete-time Kyle models with multiple informed traders using mathematical proofs.
result Equilibrium exists and converges to continuous-time equilibrium as the number of trading times increases.
Model equilibrium price in intraday electricity markets with uncertainty.
problem Formulate equilibrium model for intraday electricity trading with balancing constraints and uncertainty.
method Develop equilibrium model with agents' balancing constraints, forecasted consumption, production uncertainties, and Markov chain outages.
result Existence and uniqueness of equilibrium price as a martingale, with insights into price formation and impact of uncertainty.
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…
Develops an equilibrium model for securities pricing in a mixed cooperative and non-cooperative market.
problem Equilibrium pricing of securities in a market with cooperative and non-cooperative agents.
method Conditional extended mean-field control for cooperative agents, mean-field model for both cooperative and non-cooperative agents.
result Existence of a unique equilibrium for both finite-agent and mean-field models under certain conditions.
A new approach to MV portfolio optimization with jumps and RL.
problem Continuous-time Mean-Variance portfolio optimization with jumps.
method Jump-diffusion process, Reinforcement Learning, time-inconsistent control (TIC), Actor-Critic RL algorithm.
result The proposed RL model is profitable in real-world market data.
Alternative finance models from physics for non-equilibrium systems.
problem Inequities of classical finance models in physics-based perspective.
method Physics-based insights for non-equilibrium finance models.
result Alternative models for non-equilibrium finance systems.
New model outperforms Neural ODEs while being more efficient.
problem Stable convergence and existence guarantees for implicit-depth models.
method Developed Monotone Operator Equilibrium Network (monDEQ) based on monotone operator theory.
result MonDEQ models outperform Neural ODEs and are more computationally efficient.
Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…
The paper proves an equilibrium in a limited stock market participation model with power utilities.
problem Existence of an equilibrium in a model with limited stock market participation and power utilities.
method Proves existence and uniqueness of a solution to a singular and path-dependent Riccati-type ODE.
result Proves existence of a Radner equilibrium with homogenous power-utility investors.
AMM finds optimal contract for LPs to maximize order flow.
problem Maximizing order flow in AMMs with LPs.
method Leader-follower stochastic game, closed-form equilibrium solutions.
result LPs incentivized to add liquidity when external price attracts more noise trading.
New systemic risk models for banks choosing their group memberships.
problem Analyzing systemic risk for banks in disjoint and overlapping groups.
method Proposed new models with realistic game features, introducing Nash equilibrium for optimal solution.
result Explicit solution for risk allocation and existence/uniqueness of Nash equilibrium.
The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Goldman model(The Journal of Finance, 1980) which we consider in this paper. We study the passage from disequilibrium dynamics to equilibrium. …
Modeling insider trading with transaction costs and fair pricing.
problem Maximizing profits for an informed trader in a market with transaction costs and fair pricing.
method Single auction model and continuous time analogue, analyzing equilibrium behavior with polynomial and differential equations.
result Equilibrium trading strategy and pricing rules are affected by transaction costs, revealing an information gap.