arXiv subjects

Eyal Neuman

Publications and source records attributed to Eyal Neuman.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Execution with Passive Market Impact

We derive a mesoscopic model for optimal execution with limit orders that incorporates microstructural features of passive price impact. Our framework is based on two empirical observables: the approximately exponential decay of limit-order fill probabilities with distance from the midprice, and the short-term linear response of price changes to order flow imbalance. Combining these ingredients, we obtain a reduced-form passive impact rate that decays exponentially with quote distance. The model describes passive execution at a tactical level, where fills arise from a sequence of quote adjustments that balance execution probability, adverse selection, and opportunity cost. We formulate and solve an optimal liquidation problem in which the trader controls the aggressiveness of passive sell quotes. This generates a trade-off between higher fill intensity and larger accumulated impact on the one hand, and lower impact but greater non-execution risk on the other. Empirical calibration using NASDAQ equities and public FX supports the empirical foundations of the model. We also analyse extensions with heterogeneous decay rates, transient impact, and target execution schedules.

q-fin.TR↗

arXiv2026

Competition in Dealer Markets with Internalisation and Externalisation

We model a market with multiple dealers who compete for client order flow by dynamically updating their bid and ask quotes for a risky asset. Dealers aim to maximise expected profits while controlling inventory risk by skewing their quotes to attract offsetting order flow (internalisation) or by directly offloading positions in the market (externalisation). Using a variational approach, we derive a closed-form equilibrium for the resulting Nash competition, shedding light on key features of dealer market dynamics. We show that dealers relying on internalisation are compelled to increase their externalisation activity when competing with externalising dealers. This strategic shift in equilibrium leads to significantly higher hedging costs for all dealers and substantially wider spreads for clients.

q-fin.TR↗

arXiv2026

Potential Games on Unimodular Random Graphs

We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and infinite-player games. A key observation is that the mass-transport principle identifies the first variation of this potential with the first-order condition of a representative (root) player. Under suitable convexity assumptions, we prove that minimizers of the potential coincide with quenched Nash equilibria, and conversely. We also establish the thermodynamic limit of the potential along weakly convergent sequences of unimodular measures. Finally, we present examples with semi-explicit equilibrium descriptions. In linear-quadratic games on unimodular graphs, equilibria are expressed in terms of the Green kernel of the simple random walk operator, while in convex settings, equilibria are characterized by solutions to nonlinear Poisson equations.

math.OC↗

arXiv2026

Stochastic Games on Large Sparse Graphs

We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both finite and countably infinite populations, with asymptotics described through local weak convergence of marked graphs. The framework allows path-dependent utility functionals that may be heterogeneous across players. Under a contraction condition, we prove existence and uniqueness of Nash equilibria and establish exponential decay of correlations with graph distance. We further show that global equilibria can be approximated by truncated local games, and can even be reconstructed exactly on subgraphs given information on their boundary. Finally, we prove convergence of Nash equilibria along locally weakly convergent graph sequences, including sequences sampled from hyperfinite unimodular random graphs.

math.OC↗

arXiv2025

FX Market Making with Internal Liquidity

As the FX markets continue to evolve, many institutions have started offering passive access to their internal liquidity pools. Market makers act as principal and have the opportunity to fill those orders as part of their risk management, or they may choose to adjust pricing to their external OTC franchise to facilitate the matching flow. It is, a priori, unclear how the strategies managing internal liquidity should depend on market condions, the market maker's risk appetite, and the placement algorithms deployed by participating clients. The market maker's actions in the presence of passive orders are relevant not only for their own objectives, but also for those liquidity providers who have certain expectations of the execution speed. In this work, we investigate the optimal multi-objective strategy of a market maker with an option to take liquidity on an internal exchange, and draw important qualitative insights for real-world trading.

q-fin.TR↗

arXiv2025

Nonparametric Estimation of Self- and Cross-Impact

We introduce an offline nonparametric estimator for concave multi-asset propagator models based on a dataset of correlated price trajectories and metaorders. Compared to parametric models, our framework avoids parameter explosion in the multi-asset case and yields confidence bounds for the estimator. We implement the estimator using both proprietary metaorder data from Capital Fund Management (CFM) and publicly available S&P order flow data, where we augment the former dataset using a metaorder proxy. In particular, we provide unbiased evidence that self-impact is concave and exhibits a shifted power-law decay, and show that the metaorder proxy stabilizes the calibration. Moreover, we find that introducing cross-impact provides a significant gain in explanatory power, with concave specifications outperforming linear ones, suggesting that the square-root law extends to cross-impact. We also measure asymmetric cross-impact between assets driven by relative liquidity differences. Finally, we demonstrate that a shape-constrained projection of the nonparametric kernel not only ensures interpretability but also slightly outperforms established parametric models in terms of predictive accuracy.

q-fin.TR↗

arXiv2025

Stochastic Graphon Games with Interventions

We consider a class of targeted intervention problems in dynamic network and graphon games. First, we study a general dynamic network game in which players interact over a graph and maximize their heterogeneous, concave goal functionals, which depend on both their own actions and their interactions with their neighbors. We establish the existence and uniqueness of the Nash equilibrium in both the finite-player network game and the corresponding infinite-player graphon game. We also prove the convergence of the Nash equilibrium in the network game to the one in the graphon game, providing explicit bounds on the convergence rate. Using this framework, we introduce a central planner who implements a dynamic targeted intervention. Given a fixed budget, the planner maximizes the average welfare at equilibrium by perturbing the players' heterogeneous objectives, thereby influencing the resulting Nash equilibrium. Using a novel fixed-point argument, we prove the existence and uniqueness of an optimal intervention in the graphon setting, and show that it achieves near-optimal performance in large finite networks, again with explicit bounds on the convergence rate. As an application, we study the special case of linear-quadratic objectives and exploit the spectral decomposition of the graphon operator to derive semi-explicit solutions for the optimal intervention. This spectral approach provides key insights into the design of optimal interventions in dynamic environments.

math.OC↗

arXiv2025

Fredholm Approach to Nonlinear Propagator Models

We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay.

q-fin.MF↗

arXiv2024

Stochastic Graphon Games with Memory

We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When the agents' interactions are modeled by a weighted graph, we formulate the corresponding non-Markovian continuum-agent game, where interactions are modeled by a graphon. We also derive the Nash equilibrium of the graphon game explicitly by first reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations, then decoupling it using the spectral decomposition of the graphon operator, and finally solving it in terms of operator resolvents. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of agents increases. This holds both when a given graph sequence converges to the graphon in the cut norm and when the graph sequence is sampled from the graphon. We also bound the convergence rate, which depends on the cut norm in the former case and on the sampling method in the latter. Finally, we apply our results to various stochastic games with heterogeneous interactions, including systemic risk models with delays and stochastic network games.

math.OC↗

arXiv2024

Fluid-Limits of Fragmented Limit-Order Markets

Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, we establish that the fluid system is asymptotically stable for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al. (2021).

math.PR↗

arXiv2024

Unwinding Toxic Flow with Partial Information

We consider a central trading desk which aggregates the inflow of clients' orders with unobserved toxicity, i.e. persistent adverse directionality. The desk chooses either to internalise the inflow or externalise it to the market in a cost effective manner. In this model, externalising the order flow creates both price impact costs and an additional market feedback reaction for the inflow of trades. The desk's objective is to maximise the daily trading P&L subject to end of the day inventory penalization. We formulate this setting as a partially observable stochastic control problem and solve it in two steps. First, we derive the filtered dynamics of the inventory and toxicity, projected to the observed filtration, which turns the stochastic control problem into a fully observed problem. Then we use a variational approach in order to derive the unique optimal trading strategy. We illustrate our results for various scenarios in which the desk is facing momentum and mean-reverting toxicity. Our implementation shows that the P&L performance gap between the partially observable problem and the full information case are of order $0.01\%$ in all tested scenarios.

q-fin.TR↗

arXiv2024

The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces

We generalize the characterization theorem going back to Mercer and Young, which states that a symmetric and continuous kernel is positive definite if and only if it is integrally positive definite, to matrix-valued kernels on separable metric spaces. We also demonstrate the applications of the generalized theorem to the field of convex optimization and other areas.

math.FA↗

arXiv2024

Optimal Portfolio Choice with Cross-Impact Propagators

We consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate this problem as the maximization of a revenue-risk functional, where the agent also exploits available information on a progressively measurable price predicting signal. We solve the maximization problem explicitly in terms of operator resolvents, by reducing the corresponding first order condition to a coupled system of stochastic Fredholm equations of the second kind and deriving its solution. We then give sufficient conditions on the matrix-valued propagator so that the model does not permit price manipulation. We also provide an implementation of the solutions to the optimal portfolio choice problem and to the associated optimal execution problem. Our solutions yield financial insights on the influence of cross-impact on the optimal strategies and its interplay with alpha decays.

q-fin.PM↗

arXiv2023

An Offline Learning Approach to Propagator Models

We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy.

math.OC↗

arXiv2023

Fast and Slow Optimal Trading with Exogenous Information

We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.

q-fin.TR↗

arXiv2023

Closed-Loop Nash Competition for Liquidity

We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.

q-fin.MF↗

arXiv2023

Equilibrium in Functional Stochastic Games with Mean-Field Interaction

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the Nash equilibrium of the game semi-explicitly in terms of operator resolvents, by reducing the associated first order conditions to a system of stochastic Fredholm equations of the second kind and deriving their solution in semi-explicit form. Furthermore, by proving stability results for the system of stochastic Fredholm equations, we derive the convergence of the equilibrium of the $N$-player game to the corresponding mean-field equilibrium. As a by-product, we also derive an $\varepsilon$-Nash equilibrium for the mean-field game, which is valuable in this setting as we show that the conditions for existence of an equilibrium in the mean-field limit are less restrictive than in the finite-player game. Finally, we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay, and optimal liquidation games with transient price impact.

math.OC↗

arXiv2023

The radius of a self-repelling star polymer

We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes $N$ Brownian motions up to time $T$, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that $T \leq N$. One of the highlights of our results is that in two dimensions, we find that the radius is proportional to $T^{3/4}$, up to logarithmic corrections. Our result may shed light on the well-known conjecture that for a single self-avoiding random walk in two dimensions, the end-to-end distance up to time $T$ is roughly $T^{3/4}$.

math.PR↗