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.
Study BSΔE on lattices for asset price analysis.
problem Optimal investment and market equilibrium analysis in asset price models.
method Backward stochastic difference equations on lattices.
result Applications to optimal investment and market equilibrium analysis.
Equilibrium found for multi-agent trading with transaction costs.
problem Designing a trading equilibrium for multiple agents with transaction costs.
method Proving the existence of a continuous-time Radner equilibrium with incentives and transaction costs.
result Each agent optimally trades for a specific time interval before stopping, influenced by transaction costs.
I propose and briefly define the concept of Urban Isobenefit Lines by using functions as easy as efficient, whose results can offer a rich tool to use into spatial equilibrium analysis involving cities. They are line joining urban points with equal level of positional advantage from city amenities. The results which on…
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.
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.
Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.
problem Solving zero-sum differential games on Riemannian manifolds.
method Analysis of two simultaneous min-max algorithms, τ-GDA and τ-SGA, to differential Stackelberg and Nash equilibria, with conditions for linear convergence and asymptotic approximation. result Established sufficient conditions for linear convergence of τ-GDA and demonstrated faster convergence of τ-SGA in some cases. This paper studies the transition from disequilibrium to equilibrium in financial markets.
problem Modeling financial markets as disequilibrium models and analyzing their transition to equilibrium.
method Mathematical analysis using asymptotic limits and Tikhonov-Fenichel reduction.
result Stability of the reduced equilibrium model and economic implications are discussed.
Deep equilibrium models estimate latent variables from data.
problem Estimating latent variables from data.
method Generalized exponential family models, deep equilibrium networks.
result Deep equilibrium models solve MAP estimates for latent and transformation parameters.
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
Paper generalizes Hardy-Rogers maps for market equilibrium analysis in duopoly markets.
problem Existence and uniqueness of market equilibrium in duopoly markets with non-differentiable, nonlinear response functions.
method Coupled fixed points approach for generalized Hardy-Rogers maps.
result Enriched understanding of market equilibrium in duopoly markets with non-differentiable response functions.
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…
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.
Extends SORTE to multivariate risk functions.
problem Analyzing systemic risk in financial institutions or insurance-reinsurance markets.
method Develops a new framework for multivariate utility functions and applies duality theory.
result Proves existence, uniqueness, and Nash Equilibrium property of Multivariate Systemic Optimal Risk Transfer Equilibrium.
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.
The paper analyzes trade dynamics among G7 countries, revealing unequal exchange and degenerate equilibrium states.
problem Unequal exchange and degenerate equilibrium states in international trade among G7 countries.
method Analysis based on a model of international trade with supply and demand structures.
result Found relative equilibrium price vector is very degenerate, indicating unequal exchange.
We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a 2−dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this i…
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.
Generalizes insider trading model to multiple assets.
problem Modeling informed trading in a multi-asset context.
method Formulated an infinite-dimensional Bayesian trading game.
result Obtained a parsimonious equilibrium with closed-form solutions.
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 ε-mixed Nash equilibrium. 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.
In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disor…
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis
problem Multidisciplinary design analysis of coupled engineering systems requires solving equilibrium states where all disciplinary coupling variables are consistent.
method Residual manifold surrogate modeling framework for coupled systems.
result REMAL learns a surrogate model of the joint residual manifold via multitask Gaussian process models.
The paper analyzes reinsurance strategies in a competitive multi-agent system.
problem Strategic interactions and competitive behavior in multi-layer reinsurance chains.
method Stochastic differential games and non-zero-sum game models to characterize strategic interactions. Dynamic programming and game theory to derive equilibrium strategies.
result Intensified competition reduces safety loadings in reinsurance contracts.
Intuitive clustering algorithm balances cluster size and cohesion.
problem Cluster definition and selection in data analysis.
method Nearest neighbours equilibrium condition for clustering.
result High-quality clustering solutions compared to benchmarks.
Study examines how market dynamics affect emissions trading prices and abatement efforts.
problem Effectiveness of emissions markets depends on regulatory standards, costs, and abatement levels.
method Radner equilibrium framework that considers intertemporal decision-making and uncertainty.
result Variations in regulatory standards, costs, and abatement levels influence allowance prices and abatement efforts.
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
The paper explores how investors make decisions under disappointment aversion, finding that they prefer not to invest.
problem Continuous-time portfolio selection under generalized disappointment aversion.
method Sufficient and necessary condition for equilibrium strategies via fully nonlinear integral equation.
result Equilibrium strategy under disappointment aversion leads to less investment in the stock market compared to classical utility theory.
Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
Graphon game model simplifies stochastic interactions among agents.
problem Complex interactions among heterogeneous agents in stochastic games.
method Introduced a discrete-time graphon game formulation with a representative player.
result Existence and uniqueness of graphon equilibrium proven with mild assumptions.
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…
During the last two years, Europe has been facing a debt crisis, and Greece has been at its center. In response to the crisis, drastic actions have been taken, including the halving of Greek debt. Policy makers acted because interest rates for sovereign debt increased dramatically. High interest rates imply that defaul…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our…
The paper solves a portfolio selection problem in incomplete markets by balancing utility and risk.
problem Time-inconsistent portfolio selection in incomplete markets.
method Characterizes equilibrium via a coupled quadratic BSDE system, introduces approximate equilibrium for general cases.
result Established existence theory for equilibrium strategies in special and general cases.
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub-additive and the state process is one-dimensional, an opt…
This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or symmetry, product costs, or linearity of the utility function. The proof is based …
Develops a game-theoretic approach to solve SGEP efficiently.
problem Efficiently solving the symmetric generalized eigenvalue problem for large datasets.
method Formulates SGEP as a Nash equilibrium in a game-theoretic context and develops a parallelizable algorithm.
result Achieves O(dk) runtime complexity, making it feasible for large-scale problems. An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an α-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect…
We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stoc…
The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. F…
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.
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …
We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to market risk tend to submit more elasti…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process, and a defaultable bond, whose prices are determined via equilibrium. We analyze fi…
Paper analyzes adversarial attacks and defenses using game theory.
problem Unclear conditions for optimal attacks and defenses in adversarial learning.
method Game-theoretic framework with locally linear decision boundary model.
result Fast Gradient Method attack and Randomized Smoothing defense form a Nash Equilibrium.
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…
Study Nash equilibrium between broker and informed trader in dealer and lit markets.
problem Nash equilibrium between broker and informed trader in dealer and lit markets with partial information.
method Convex analysis, FBSDEs, polynomial approximation.
result Existence and uniqueness of Nash equilibrium for short time horizons.
In this paper, we analyze Nash equilibria between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a…