dynamic fee design

This study investigates how liquidity providers in automated market makers can dynamically set trading fees to balance impermanent loss against rebalancing gains. Building upon the Loss-versus-Rebalancing (LVR) framework, the fee-setting strategy is modeled as a controlled stochastic process. By solving the associated Hamilton–Jacobi–Bellman equation and incorporating ergodic control, finite-difference methods, and impulse control to account for gas costs, the authors propose a procyclical dynamic fee mechanism that scales positively with volatility. This mechanism admits both closed-form structure and numerical solutions under stochastic volatility and exhibits optimality independent of risk preferences. Empirical calibration demonstrates that the proposed strategy weakly dominates static or heuristic volatility-linked fee schemes across all simulated paths, significantly enhancing long-term wealth growth while keeping gas costs negligible.

This study addresses the lack of empirical evidence for optimal execution in automated market makers (AMMs) under dynamic trading fees. The authors propose a closed-loop simulator grounded in equilibrium theory, incorporating constant-product liquidity pools with dynamic fees, fee-sensitive noise trading flows, and an analytical arbitrage mechanism, thereby enabling counterfactual analysis in a controlled environment. Using deep Q-networks (DQN), they compare reinforcement learning against multiple benchmark strategies and find that DQN significantly outperforms traditional scheduling and planning methods only in dynamic-fee settings. Across 1,000 held-out random seeds, DQN consistently reduces execution shortfall across all order sequencing configurations, achieving a 13.3 basis point improvement in the agent-last setting, while showing no significant advantage under constant fees.

This study investigates the causal impact of protocol fee changes on liquidity provision behavior in automated market makers, effectively disentangling confounding factors such as fee revenue, adverse selection, and routing responses. Leveraging Uniswap’s fee switch event, the authors employ a matched overlapping event study combined with a difference-in-differences design, constructing a hash-verified panel dataset from on-chain logs. This approach enables the first identification of liquidity providers’ (LPs’) genuine responses to reduced fee splits and clearly delineates LP behavior from trader-side dynamics under variable fee mechanisms. The paper introduces a channel admissibility audit framework and finds no significant short-term effects on liquidity supply, depth, or LP composition, suggesting limited efficacy of fee adjustments under current mechanisms; however, Token-1 trading volume and native fee revenue violate the parallel trends assumption.

This study addresses the significant loss in liquidity value (LVR) experienced by liquidity providers (LPs) in concentrated liquidity automated market makers like Uniswap v3, which stems from adverse selection and is inadequately compensated by existing fee mechanisms. To tackle this challenge, the authors propose and evaluate a dynamic fee mechanism that integrates volatility and order flow toxicity metrics. For the first time, they develop a multi-agent simulation framework grounded in realistic on-chain microstructure, incorporating a Heston stochastic volatility market model, block propagation delays, and heterogeneous participant behaviors—including MEV searchers and smart routing strategies. Experimental results demonstrate that the proposed mechanism substantially increases LP fee revenue under price lag risk, enabling their hedged PnL to turn positive, thereby validating the efficacy of dynamically compensating for LVR rather than attempting its complete elimination.

Automated Market Makers (AMMs) in DeFi face adverse selection in blue-chip asset pairs: arbitrage—while essential for revenue—is also a primary source of losses due to “informed order flow.” Method: We develop a differential-equation-based arbitrage dynamics model, integrating sensitivity analysis and numerical simulation to systematically quantify how fee structures affect arbitrage behavior, uninformed trading incentives, and net revenue. Contribution/Results: We propose a directional dynamic fee mechanism—where fees adjust asymmetrically with price movement direction—to suppress toxic flow while preserving benign liquidity. Our analysis reveals that the optimal static fee lies within a narrow range; in contrast, the dynamic mechanism increases AMM net revenue by 18–32% empirically and reduces adverse selection losses by over 40%. This work provides a theoretically grounded, empirically testable framework for AMM fee design.

This work addresses the limitations of existing transaction fee mechanisms, such as EIP-1559, which lack explicit modeling of transaction dynamics in the mempool and thus struggle to achieve efficient scheduling and pricing. The paper formulates transaction scheduling as a Markov decision process for the first time and proposes a dynamic pricing mechanism that integrates primal-dual optimization analysis with natural policy gradient methods to maximize long-term discounted revenue while accounting for holding costs and overcapacity penalties. Theoretical analysis reveals the dual optimization nature underlying EIP-1559 and establishes that the optimal policy exhibits either a threshold structure or Bang-Bang control characteristics. Empirical results demonstrate that the proposed mechanism effectively stabilizes the mempool, drives average scheduled transaction volume toward the target block capacity, and recovers the EIP-1559 update rule under specific conditions.

This study investigates the performance trade-offs of data-driven approaches in finite-horizon dynamic pricing, with a focus on complex settings involving high-dimensional multi-product offerings, heterogeneous demand structures, and intertemporal revenue constraints. By systematically comparing Fitted Dynamic Programming (Fitted DP) against several reinforcement learning algorithms—integrating demand estimation, trajectory sampling, and expectation-based optimization—the work comprehensively evaluates their relative strengths in terms of revenue generation, stability, constraint satisfaction, and computational scalability. The findings reveal that Fitted DP exhibits superior scalability in structured, complex environments, whereas reinforcement learning demonstrates greater flexibility and adaptability. These insights provide both theoretical grounding and empirical evidence to inform method selection for real-world dynamic pricing systems.

研究通过控制实验，探讨了基于规则的定价算法设计如何影响市场结果，采用警告、预设策略和大语言模型建议等方法，发现这些设计普遍提高了市场价格。

This study addresses the challenge of executing large orders in continuous double-auction markets under time and liquidity constraints. The authors propose a risk-constrained model predictive control (MPC) framework that dynamically optimizes trading decisions via quadratic programming while tracking benchmark schedules such as TWAP or VWAP. The approach permits strategic deviations from the benchmark to minimize expected execution cost, explicitly incorporating benchmark residual cost into the objective function to enable modular, data-driven deployment in live trading environments. Empirical evaluation using six months of NASDAQ Level 3 data demonstrates that the method reduces execution schedule gaps by 40–50% compared to cross-price benchmarks and significantly mitigates slippage. Performance improves further when integrated with price forecasts.

This work addresses a key limitation of existing automated market makers (AMMs) in prediction markets: while they bound the worst-case total loss for subsidy providers, they offer no control over how this loss is distributed across price and time. Building upon the loss-versus-rebalancing (LVR) framework, the paper introduces the first uniform-loss AMM, whose instantaneous LVR is proportional to the pool value and independent of the current price. By establishing a bidirectional correspondence between winning martingales and pricing functions, and integrating dynamic liquidity management, the proposed mechanism enables on-demand shaping of the expected cumulative loss trajectory. The authors theoretically prove the existence of uniform-LVR pricing functions under general winning martingales and validate the approach through representative examples, offering a novel tool for controlling loss distribution in AMM design.