Market Making

Market makers play a vital role in ensuring efficient trade within financial markets. Recent literature has delved into training market-making systems using reinforcement learning. This paper delves into the impact of various loss function formulations on risk management behavior within reinforcement-based market making. Through empirical evaluation, we contrast profit-maximizing strategies with risk-averse approaches, finding that penalties for inventory and cash management foster more resilient and adaptable market-making strategies. Our results underscore the significance of striking a balance between profit maximization and risk management in algorithmic trading, providing actionable insights for refining strategies in practical settings.

Automated markets increasingly route order flow from learning trading agents through automated market makers (AMMs). We model trader archetypes as AI agents defined by their reward functions and analyze the feedback they create on a constant-product AMM. Herd-dominated and arbitrage-dominated markets of equal size have identical return distributions and turnover, so no rule based on volatility, value-at-risk, stress frequency, or volume can tell them apart; yet their stress episodes differ in length by a factor unbounded in the feedback-to-noise ratio $β/s$. Serial statistics identify the feedback sign from $Θ((s/β)^2\log(1/δ))$ observations, and this rate is tight. When agents trade together, profit-seeking agents ride herds rather than lean against them, leading to all-or-nothing participation. Spread-earning market makers restore stability but make liquidity fragile, with discontinuous collapse and hysteresis; maker--taker pricing, not a uniform fee, is the effective instrument.

We propose a market-making game played among $N \ge 2$ strategic market makers and a single non-strategic representative trader. In a continuous quote space, standard finite-game arguments do not apply, while non-convex and discontinuous payoffs rule out classical continuous existence results and complicate learning. Nonetheless, we characterize pure-strategy Nash equilibria (PSNEs) and show that at least one PSNE always exists under minimal assumptions on the underlying asset value distribution, and that the equilibrium bid-ask spread widens strictly with asset value volatility. To obtain a tractable learning framework, we discretize prices and, under an additional regularity condition, show that the time-averaged play of no-internal-regret learners approaches the continuous Nash price envelope as the tick size vanishes. Finally, we empirically validate our theoretical results through numerical simulations.

A market maker provides liquidity by quoting prices to buy and sell an asset, earning the spread while managing inventory risk. We study market makers trained with multi-agent reinforcement learning on prediction markets, specifically Polymarket, whose thin order books pose distinct challenges. Three challenges underpin this research: adverse selection may cause a policy trained on real data to stop quoting; the consequences of a quote can arrive many steps after the action; and prediction-market L2 data does not identify individual orders needed for simulation. We address these challenges by reconstructing order-level LOBSTER-format data from Polymarket and training agents in JaxMARL-HFT on 417 real markets. We enrich the baseline market maker's observation space with the book and recent flow, redesign its actions and inventory controls, and propose a cooperative multi-agent decomposition into a quoter and a risk manager trained using recurrent Independent Proximal Policy Optimisation (IPPO) with RNN policies. We investigate reward shaping, particularly reward blending and post-fill markout, to mitigate credit-assignment difficulties between the agents. Our redesigned single-agent market maker quotes more frequently and incurs smaller held-out losses than the retrained JaxMARL-HFT baseline, although the contributions of jointly changed observations, actions and risk constraints are not separately identified. Decomposition alone performs poorly; careful reward design substantially improves the desk relative to the unshaped split and yields our best result. Models are evaluated on realised end-of-episode portfolio value on held-out markets. None establishes positive average portfolio value in periodic held-out evaluation, and each configuration was trained with one seed. The environment, data and protocol lay a foundation for makers that quote many linked markets at once.

Market makers keep trading efficient by setting bid and ask prices for buyers and sellers. In sequential market making, trades happen independently based on price thresholds, requiring the market maker to maintain balanced, low-risk inventory over T rounds. This paper studies how to maximize revenue with unknown buyer and seller valuations using regret minimization. When the market maker only sees trade success or failure, an algorithm achieves regret and inventory bounds proportional to T to the power of 2/3. When full order book data is available for failed trades, regret and inventory limits improve significantly to the square root of T. We also establish a fundamental trade-off via a lower bound, by proving that tighter round-by-round inventory limits strictly force higher minimum regret.

Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.

Market-making strategies in real limit order book markets face substantial model uncertainty and regime-shift risk. Existing adversarial reinforcement learning approaches improve robustness by formulating the Avellaneda--Stoikov market-making problem as a zero-sum game between a market maker and an environmental adversary. However, these approaches typically rely on Poisson order arrivals and neglect trade-induced price impact, limiting their ability to capture important high-frequency market microstructure effects such as clustered order flow, self-excitation, and post-trade price feedback. We extend adversarial reinforcement learning for market making to a more complex environment with Hawkes self-exciting order arrivals and trade-induced price impact. To mitigate the increased non-stationarity introduced by the expanded regime space, we incorporate an LSTM module that explicitly models the temporal structure of recent observations. We further characterize the equilibrium properties of the proposed framework through both game-theoretic analysis and numerical experiments, and introduce a robustness evaluation protocol focused on improvements in the left tail of the return distribution. Experimental results across a range of market regimes show that the proposed method achieves improved left-tail performance in most complex microstructure environments. In particular, the gains are pronounced in regimes with strong Hawkes excitation and low-to-moderate price impact. Bootstrap tests provide no evidence that these improvements are obtained through a stronger terminal directional inventory bias. These results suggest that combining adversarial training with temporal state representation can improve the robustness of reinforcement-learning-based market-making strategies under order-flow self-excitation, price impact, and regime uncertainty.

We describe an adaptive market-making architecture that preserves the analytical structure of the Avellaneda--Stoikov framework while introducing a successor measure-style adaptation mechanism. In our paper we keep Avellaneda--Stoikov fast Hamilton--Jacobi--Bellman structure and make it adaptive to changing market regimes and trading objectives. The central idea is to separate market dynamics from the trading objective. The market state determines a low-dimensional set of Avellaneda--Stoikov parameters, while recent realized rewards determine a low-dimensional objective vector. The HJB forward map then converts this objective into optimal bid and ask quotes through a scalarization of future reward features.

We develop a rigorous theoretical framework for optimal market making in perpetual futures markets with zero maker fees. We model the market maker's problem as a stochastic optimal control problem on a filtered probability space, where the controls are adaptive bid-ask spreads and inventory hedging decisions across two exchanges. Our contributions include: (i) a PnL decomposition theorem separating revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure; (ii) the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem; (iii) High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula; (iv) analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds; (v) optimal cross-exchange hedging policies with funding rate dynamics and a hedge regime trichotomy; (vi) a robustness margin quantifying parameter uncertainty tolerance; (vii) exponential drawdown probability bounds and a universal APY-VaR identity; (viii) ergodic inventory distribution under optimal control with Bayesian adaptive estimation; (ix) Kelly-optimal leverage with ruin boundaries; and (x) multi-pair portfolio allocation with diversification saturation results. Numerical analysis with twenty-three figures reveals phase transitions between profitable and unprofitable regimes. Our framework unifies and extends the Avellaneda-Stoikov, Gueant-Lehalle-Fernandez-Tapia, and Glosten-Milgrom paradigms for modern decentralized venue microstructure.