Market Microstructure

We study the perfect information Nash equilibrium between a broker and her clients – an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with t

Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case. While constructing the solu

Minimizing execution costs for large orders is a fundamental challenge in finance. Firms often depend on brokers to manage their trades due to limited internal resources for optimizing trading strategies. This paper presents a methodology for evaluating the effectiveness of broker execution algorith

We consider an Ito-financial market at which the risky assets’ returns are derived endogenously through a market-clearing condition amongst heterogeneous risk-averse investors with quadratic preferences and random endowments. Investors act strategically by taking into account the impact that their o

This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This generalizes previous results that used convexity, and also g

Market fluctuations caused by overtrading are important components of systemic market risk. This study examines the effect of investor sentiment on intraday overtrading activities in the Chinese A-share market. Employing high-frequency sentiment indices inferred from social media posts on the Eastmo

Investors and regulators can greatly benefit from a realistic market simulator that enables them to anticipate the consequences of their decisions in real markets. However, traditional rule-based market simulators often fall short in accurately capturing the dynamic behavior of market participants,

We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calc

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,

Automated market makers (AMMs) have emerged as the dominant market mechanism for trading on decentralized exchanges implemented on blockchains. This paper presents a single mechanism that targets two important unsolved problems for AMMs: reducing losses to informed orderflow, and maximizing revenue

We present a formal framework for the aggregation of financial markets mediated by arbitrage. Our main tool is to characterize markets via utility functions and to employ a one-to-one correspondence to limit order book states. Inspired by the theory of thermodynamics, we argue that the arbitrage-med

There is a persistent lack of funding, especially for SMEs, that cyclically worsens. The factoring and invoice discounting market appears to address delays in paying commercial invoices: sellers bring still-to-be-paid invoices to financial organizations, intermediaries, typically banks that provide

Calibration of option pricing models is routinely repeated as markets evolve, yet modern systems lack an operator for removing data from a calibrated model without full retraining. When quotes become stale, corrupted, or subject to deletion requirements, existing calibration pipelines must rebuild t

Consider a finite set of trade orders and automated market makers (AMMs) at some state. We propose a solution to the problem of finding an equilibrium price vector to execute all the orders jointly with corresponding optimal AMMs swaps. The solution is based on Brouwer’s fixed-point theorem. We disc

Silkswap is an automated market maker model designed for efficient stablecoin trading with minimal price impact. The original purpose of Silkswap is to facilitate the trading of fiat-pegged stablecoins with the stablecoin Silk, but it can be applied to any pair of stablecoins. The Silkswap invariant

We analyse two models of liquidity provision to determine the retail traders’ preference for marketable order routing. Order internalization is captured by a model of market makers competing for the retail order flow in a Bertrand fashion. On the other hand, the price-taking competitive liquidity pr

We study liquidity provision in automated market makers when trading in the external market incurs proportional transaction costs. We consider both separately collected fees and fees retained in reserves. The benchmark is a self-financing strategy holding the same total risky inventory and trading a

The tendency of the double auction mechanism to drive prices to competitive equilibrium has been well documented in laboratory experiments, but the phenomenon has lacked a theoretical explanation. This paper studies dynamic double auctions in a pure exchange economy where agents bid their indifferen

Prediction markets offer a natural testbed for trading agents: contracts have binary payoffs, prices can be interpreted as probabilities, and realized performance depends critically on market microstructure, fees, and settlement risk. We introduce PredictionMarketBench, a SWE-bench-style benchmark f

We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit time-discretization scheme coupled with a policy iteration algori