arXiv research

Study shows unique linear equilibrium in market with constrained trader.

Study Nash equilibrium in non-zero-sum game with Bermudan strategies.

We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and …

DEQs converge to optimal solutions with mild over-parameterization.

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

Study how transaction costs impact stock returns and holdings in equilibrium.

Gradient descent dynamics studied for DEQs in linear and single-index models.

Policy gradient methods find Nash equilibrium in noisy games.

A firm with heterogeneous shareholders optimizes dividends under ambiguity aggregation.

Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.

This paper extends the convergence rate of DEQs with ReLU to any general activation.

In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional…

Study equilibrium consumption habits in a large population using mean field games.

Optimal algorithm for two-player zero-sum games with linear parameterization.

New results on financial equilibria in markets with general semimartingales.

In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution withi…

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled…

The paper explains how to predict returns based on firm characteristics.

Kernel method approximates Koopman operator eigenfunctions.

Study reveals dynamics of neural networks with normalization, weight decay, and SGD.

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 $N$-dimensional multi-agent economic system implies the exponential (Boltzmann-Gibss) wealth distribution an…

Despite the considerable success enjoyed by machine learning techniques in practice, numerous studies demonstrated that many approaches are vulnerable to attacks. An important class of such attacks involves adversaries changing features at test time to cause incorrect predictions. Previous investigations of this proble…

Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.

Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the mo…

We derive asset pricing formula for markets with incomplete information and subjective views.

In optimization, the negative gradient of a function denotes the direction of steepest descent. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. In this work, we show that these orthogonal directions that are ignored by gradient descent can be critical in equilibri…

This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The un…

Investors' strategies in a market influenced by price impact are analyzed, showing aggressive behavior when impact exceeds a critical point.

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost functions, while the aggregated effect of the agents is captured by the population mean o…

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 who engages in order splitting to reach a cumulative trading target and an uncon…

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 …

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric ex…

Study solves HJB equations for time-inconsistent control problems.

This work presents a methodology for forward electricity contract price projection based on market equilibrium and social welfare optimization. In the methodology supply and demand for forward contracts are produced in such a way that each agent (generator/load/trader) optimizes a risk adjusted expected value of its re…

In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional Itô calculus approach, we overcome the non-Markovian and non-semimartingale difficulty in Volterra processes. The equilibrium strategy is the…

Modeling insider trading with transaction costs and fair pricing.

Paper characterizes equilibrium strategies for stochastic control with higher-order moments.

We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally…

New model explains market dynamics with phase transitions and non-linear interactions.

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…

This paper tackles learning Stackelberg equilibrium in asymmetric games efficiently from noisy samples.

The paper solves TIC LQ control problems using stochastic differential games.

Paper analyzes adversarial attacks and defenses using game theory.

New model outperforms Neural ODEs while being more efficient.

Model shows phase transitions in asset pricing with market maker incentives.

Investigates portfolio selection among competitive agents with mean-variance preferences.

Study on liquidation games with market drop-out, proving unique equilibria.

The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.