The paper explores centroids and static equilibrium points in non-Euclidean geometries.
problem Investigating centroids and static equilibrium points in spherical, hyperbolic, and normed spaces.
method Extending Gal'perin's work, the paper examines convex bodies in these spaces and analyzes the minimum number of equilibrium points.
result Every plane convex body in any of these spaces has at least four equilibrium points, and there are mono-monostatic convex bodies in 3D spherical, hyperbolic, and certain normed spaces.
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.
Wariness affects poverty traps and equilibrium diversity in economic models.
problem The impact of wariness on poverty traps and equilibrium diversity in economic models.
method An overlapping generations model to explore the effects of wariness on poverty traps and equilibrium diversity.
result Wariness can amplify or mitigate the likelihood of poverty traps and can lead to multiple intertemporal equilibria.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant n-discretrizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We show that as n approaches infinity these numbers fluctuate around specific val…
This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered. Furthermore, the results obtained are applied to the optimality pricing. Again three …
The paper solves three problems related to monostable polyhedra.
problem Three problems related to monostable polyhedra posed by Conway and Goldberg.
method General theorem describing approximations of smooth convex bodies by convex polyhedra in terms of static equilibrium points.
result Existence of a convex polyhedron with only one stable and one unstable point.
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifol…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant n-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to…
We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash e…
Study risk-averse insider's behavior in dynamic signal asset pricing.
problem Analyzing risk-averse insider's dynamic signal in asset pricing.
method Employing a weak conditioning methodology to construct a Schrödinger bridge, deriving necessary conditions for equilibrium.
result Derive explicit closed-form solutions for important cases.
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.
New method reconstructs non-equilibrium stochastic systems from data.
problem Reconstructing non-equilibrium stochastic systems from ensemble measurements.
method Schrödinger bridge problem with multivariate Ornstein-Uhlenbeck process.
result Simulation-free algorithm achieves higher accuracy than competing methods.
We develop a formalism to study linearized perturbations around the equilibria of a pure exchange economy. With the use of mean field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that i…
This paper extends a Kyle model to include price-responsive traders, revealing new dynamics and equilibria.
problem Real-world market dynamics involve price-responsive traders, affecting market equilibrium and insider profits.
method Developed a continuous-time Kyle model with two types of price-responsive traders (momentum and contrarian), leading to a forward-backward Riccati system for equilibrium.
result The model shows that feedback effects can lead to multiple equilibria and amplify price informativeness.
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property)…
New discrete-time model shows insider trading dynamics.
problem Modeling insider trading with discrete time and noise traders.
method Formulated as a game with three types of traders, including an insider, noise traders, and a market maker. Proved existence of sequential Kyle equilibrium for various distributions and information flows.
result Equilibria exist in mixed strategies but not in pure strategies, unlike in Kyle's original model.
DQN outperforms static policies in a dynamic fee environment for automated market makers.
problem How automated market makers (AMMs) perform under dynamic fees is unknown.
method Constructed a closed-loop simulator with dynamic fees, noise flow, and arbitrage.
result A small DQN policy outperforms static policies in a dynamic fee environment.
We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We then consider the static case, which describes crystalline bodies in equilibriu…
Equilibrium Propagation (EP) is a biologically inspired learning algorithm for convergent recurrent neural networks, i.e. RNNs that are fed by a static input x and settle to a steady state. Training convergent RNNs consists in adjusting the weights until the steady state of output neurons coincides with a target y. Con…
Study a market with uncertain informed traders, finding price impact depends on both asset value and informed trader count distribution.
problem Uncertain participation of informed traders in a market with limit orders.
method Characterized equilibrium by a fixed point integral equation, analyzed large order asymptotics, solved numerically.
result Equilibrium price impact depends on both asset value and distribution of informed traders, not just expected number of informed traders.
We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 minutes) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of …
In this paper, we study the problem of sampling from a graphical model when the model itself is changing dynamically with time. This problem derives its interest from a variety of inference, learning, and sampling settings in machine learning, computer vision, statistical physics, and theoretical computer science. Whil…
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…
We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually redu…
The aim of this research is to introduce a novel structural design process that allows architects and engineers to extend their typical design space horizon and thereby promoting the idea of creativity in structural design. The theoretical base of this work builds on the combination of structural form-finding and state…
The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian n-manifold (M,g) and a positive function N, called the lapse. We study this problem o…
Prediction markets show considerable promise for developing flexible mechanisms for machine learning. Here, machine learning markets for multivariate systems are defined, and a utility-based framework is established for their analysis. This differs from the usual approach of defining static betting functions. It is sho…
Unified framework for estimating reward functions in competitive games.
problem Estimating unknown reward functions in competitive games.
method Unified framework with entropy regularization for reward function recovery.
result Strong theoretical guarantees and practical effectiveness demonstrated.
EP algorithm improved for CNNs and real-time learning.
problem EP's long simulation times and non-local learning rule limitations.
method Discrete-time formulation, continual weight updates, local time information.
result C-EP achieves best performance on MNIST with CNNs.
Study on investment strategy for agents with periodic preferences and discounting.
problem Investment decisions by agents with periodic S-shaped preferences and present bias.
method Infinite-horizon, continuous-time portfolio selection problem with quasi-hyperbolic discounting.
result Time-consistent planning strategy can be formulated as an equilibrium to a static mean field game.
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition,…
Forward hedging reshapes incentive provision in firms.
problem How does forward hedging affect incentive provision in firms?
method We consider a CARA framework to jointly characterize optimal production, compensation, and static hedging in equilibrium.
result Delegation and external hedging are partial substitutes, and delegation can increase firm value even when the agent is more risk averse.
Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of…
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…
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
problem Classifying the dimension of static potentials on 3-manifolds.
method Analysis of relative zero sets of static potentials, using Miao and Tam's technique.
result Proves one-dimensionality of static potentials under specific conditions.
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…
New bounds on trajectory safety in training models with Langevin Dynamics.
problem Bounding the probability of a model's trajectory staying away from a designated failure region.
method Analyzes Langevin dynamics on smooth, strongly convex loss landscapes, introducing shape-free and local relaxation bounds.
result The in-set probability relaxes to the static value after a burn-in time of order d, using only the global spectral gap of the loss.
New static vacuum metrics confirmed for near Euclidean boundary data.
problem Establishing sufficient conditions for near Euclidean boundary data in static vacuum metrics.
method Using new arguments from studying the conjecture for arbitrary static vacuum metrics.
result Any hypersurface in a dense subfamily is static regular.
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.
Extends static vacuum metrics with specific boundary conditions.
problem Proving the existence of static vacuum metrics with prescribed boundary data.
method Introducing static regular types (I) and (II), showing local well-posedness, and confirming Bartnik's conjecture.
result Confirms Bartnik's static vacuum extension conjecture for a broad range of boundary conditions.
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.
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.
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.
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…