arxiv: 2605.06405 · v1 · submitted 2026-05-07 · 💱 q-fin.MF

Recognition: unknown

Funding-Aware Optimal Market Making for Perpetual DEXs

Nam Anh Le

Pith reviewed 2026-05-08 03:17 UTC · model grok-4.3

classification 💱 q-fin.MF

keywords market makingperpetual contractsfunding ratesoptimal controlHJB equationliquidity provisionDEXstochastic processes

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The pith

Incorporating stochastic funding rates into the control problem improves optimal quotes for perpetual DEX market making.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that market makers in perpetual contracts must treat the funding rate as an additional stochastic state because inventory size directly determines both price exposure and ongoing funding cash flows. A sympathetic reader would care since classical models that ignore funding can produce quotes that leave unnecessary risk on the table while missing a systematic cash-flow channel. The author reduces the problem to an inventory-funding control formulation, solves it with a monotone finite-difference HJB scheme, calibrates the funding process on Hyperliquid ETH, BTC, and SOL data, and shows in holdout simulations that the resulting bid and ask offsets raise mean performance while cutting inventory fluctuations for the two largest assets.

Core claim

The central claim is that the funding-augmented value function yields quote offsets recovered from discrete inventory differences that, under two official-fill proxy calibrations, produce higher mean returns and lower root-mean-square inventory levels than the classical Avellaneda-Stoikov strategy in 100-seed simulations for ETH and BTC perpetuals on Hyperliquid.

What carries the argument

The reduced inventory-funding control problem whose solution via monotone finite-difference HJB yields state-dependent bid and ask offsets from value-function differences.

If this is right

Higher mean performance for ETH and BTC liquidity provision once funding cash flows are included in the objective.
Reduced root-mean-square inventory exposure relative to the classical model without funding dynamics.
Positive performance gains for SOL versus the unscaled classical benchmark, though not a strict Pareto improvement against a risk-scaled version.
A practical numerical route to recover optimal offsets directly from the solved value function on a discrete inventory grid.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Platforms could embed the funding state into real-time quoting engines so that market makers automatically tighten or widen spreads when funding rates move sharply.
The same reduced-control approach may extend to other stochastic cash-flow terms such as borrowing fees or liquidation penalties that scale with position size.
Out-of-sample tests on live order-book data would show whether the simulated fill proxies translate into actual execution advantages.

Load-bearing premise

That a Gaussian Ornstein-Uhlenbeck diffusion for the funding rate remains sufficient to derive and test the optimal quotes even though real funding innovations exhibit heavy tails.

What would settle it

A side-by-side simulation or live-trading comparison in which the funding-aware quotes lose their mean-performance or inventory-RMS advantage once the funding process is replaced by an OU-plus-jump model calibrated to the same data.

Figures

Figures reproduced from arXiv: 2605.06405 by Nam Anh Le.

**Figure 1.** Figure 1: Cross-asset funding diagnostics used by the HJB calibration. Funding mean-reversion view at source ↗

**Figure 2.** Figure 2: Final one-hundred-seed holdout comparison. The left panel reports paired final-equity view at source ↗

**Figure 3.** Figure 3: Seed-level final-equity delta of the finite-difference HJB policy relative to view at source ↗

read the original abstract

This paper studies optimal liquidity provision for perpetual contracts when the funding rate is a stochastic state variable. The core extension to classical market making is the coupling between inventory and funding payments: inventory creates both mark-to-market exposure and a state-dependent funding cash flow. A reduced inventory-funding control problem is formulated, solved with a monotone finite-difference Hamilton-Jacobi-Bellman scheme, and bid and ask quote offsets are recovered from discrete inventory value differences. Funding is calibrated on Hyperliquid ETH, BTC, and SOL perpetual data. Gaussian OU funding is retained as a tractable diffusion baseline, while OU-plus-jump diagnostics document the heavy-tailed funding innovations that should enter a future extension. In 100-seed holdout simulations under two official-fill proxy calibrations, the funding-aware HJB improves mean ETH/BTC performance while lowering inventory RMS relative to classical Avellaneda-Stoikov. SOL gains are positive versus unscaled AS but are not a Pareto improvement once a risk-scaled AS diagnostic is included.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds stochastic funding as a state variable coupled to inventory in the perpetual DEX market-making problem, which is a clean extension, but the simulations rest on a Gaussian OU model the authors know misses the heavy tails.

read the letter

The core advance is treating funding payments as an explicit stochastic cash flow tied to inventory size inside the optimal control setup. This goes beyond the usual Avellaneda-Stoikov inventory penalty by making the funding rate itself a state variable that affects the value function and the recovered bid/ask offsets. They reduce the problem, solve the HJB with a monotone finite-difference scheme, calibrate on Hyperliquid ETH/BTC/SOL data, and run 100-seed holdout tests under two fill proxies. For ETH and BTC the funding-aware quotes improve mean performance and cut inventory RMS relative to plain AS; SOL shows gains but not against a risk-scaled AS check. That is useful concrete work on a real feature of perpetuals. The limitation is the funding process. The abstract records that OU-plus-jump diagnostics pick up heavy-tailed innovations, yet both the HJB derivation and the reported simulations keep the plain Gaussian OU. Because the offsets are extracted from discrete value differences, the mismatch between assumed and actual funding dynamics directly shapes the claimed outperformance. They correctly flag the jumps as future work, but this leaves the numerical results conditional on a baseline the data already questions. The paper is aimed at people doing optimal control or liquidity provision in crypto derivatives. A reader who wants to see how funding enters the HJB and how the numerics are set up will get something usable from it. The formulation and the simulation protocol are clear enough that it deserves a serious referee, with the main request being either to bring the jumps into the model or to test how sensitive the quotes are to the diffusion assumption.

Referee Report

2 major / 1 minor

Summary. The paper extends classical Avellaneda-Stoikov market making to perpetual DEXs by coupling inventory with a stochastic funding rate state variable. It formulates a reduced inventory-funding control problem, solves it via a monotone finite-difference HJB scheme, calibrates a Gaussian OU funding process on Hyperliquid ETH/BTC/SOL data, and reports that in 100-seed holdout simulations the funding-aware quotes improve mean performance for ETH/BTC while reducing inventory RMS relative to classical AS (with SOL results positive versus unscaled AS but not versus risk-scaled AS).

Significance. If the simulation results are robust, the work supplies a tractable numerical method for liquidity provision that internalizes funding cash flows, a distinctive feature of perpetual contracts. The calibration on real exchange data, explicit holdout protocol, and retention of the Gaussian OU as a documented baseline for future jump extensions are constructive elements that support applicability in DeFi perpetual markets.

major comments (2)

[Abstract / Model formulation] Abstract and funding-model section: The manuscript documents heavy-tailed funding innovations via OU-plus-jump diagnostics yet derives the HJB value function and recovers bid/ask offsets exclusively under the Gaussian OU diffusion. Because the optimal quotes are obtained from discrete inventory-value differences under this process, any systematic mismatch with empirical funding dynamics directly affects the computed policy and the claimed outperformance versus Avellaneda-Stoikov in the holdout simulations.
[Simulation results] Simulation-results paragraph: The reported improvements in mean ETH/BTC performance and inventory RMS are stated without accompanying magnitudes, standard errors across the 100 seeds, or formal statistical tests. This omission prevents assessment of whether the gains are economically material or sensitive to the two official-fill proxy calibrations.

minor comments (1)

[Abstract] Clarify the precise definition of 'mean performance' (e.g., cumulative P&L, Sharpe, or other metric) and 'inventory RMS' when comparing the funding-aware HJB to both unscaled and risk-scaled Avellaneda-Stoikov baselines.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will make revisions to clarify modeling assumptions and strengthen the reporting of simulation results.

read point-by-point responses

Referee: [Abstract / Model formulation] Abstract and funding-model section: The manuscript documents heavy-tailed funding innovations via OU-plus-jump diagnostics yet derives the HJB value function and recovers bid/ask offsets exclusively under the Gaussian OU diffusion. Because the optimal quotes are obtained from discrete inventory-value differences under this process, any systematic mismatch with empirical funding dynamics directly affects the computed policy and the claimed outperformance versus Avellaneda-Stoikov in the holdout simulations.

Authors: We agree that the HJB value function and resulting bid/ask offsets are derived exclusively under the Gaussian OU funding process, as stated in the model section. The OU-plus-jump diagnostics are provided to document empirical heavy tails and to motivate future extensions, but the current policy and simulation comparisons are conditional on the OU specification. To address the concern, we will revise the abstract to explicitly state that the funding-aware quotes are obtained under the Gaussian OU diffusion and that the reported improvements versus classical Avellaneda-Stoikov hold under this modeling choice. revision: yes
Referee: [Simulation results] Simulation-results paragraph: The reported improvements in mean ETH/BTC performance and inventory RMS are stated without accompanying magnitudes, standard errors across the 100 seeds, or formal statistical tests. This omission prevents assessment of whether the gains are economically material or sensitive to the two official-fill proxy calibrations.

Authors: The referee is correct that the simulation paragraph reports only directional improvements without magnitudes, standard errors, or statistical tests. In the revised manuscript we will add the mean performance differences, standard errors computed across the 100 seeds, and p-values from paired statistical tests for the ETH/BTC and SOL comparisons under both official-fill proxy calibrations. This will allow readers to evaluate economic significance and sensitivity to the calibration choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; HJB derivation and simulation testing are independent

full rationale

The paper's core chain is: (1) formulate reduced inventory-funding stochastic control problem coupling inventory to stochastic funding cash flows; (2) solve numerically via monotone finite-difference HJB scheme; (3) recover bid/ask offsets from discrete value-function differences; (4) calibrate Gaussian OU parameters on Hyperliquid data solely for Monte-Carlo simulation testing; (5) compare funding-aware quotes against classical Avellaneda-Stoikov in 100-seed holdout simulations. None of these steps reduce to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation. The improvement claim is a model-consistent validation that the funding state variable adds value relative to the funding-ignorant benchmark; it is not forced by construction of the inputs. Calibration enters only post-derivation for testing, satisfying the independence criterion.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based on the abstract alone, the central claim rests on a stochastic control formulation whose solution is obtained numerically; the funding process is treated as an exogenous diffusion calibrated to historical data.

free parameters (1)

OU drift and volatility parameters for funding rate
Calibrated directly to Hyperliquid ETH, BTC, and SOL perpetual data to drive the simulation baseline.

axioms (2)

domain assumption Funding rate dynamics can be approximated by a Gaussian Ornstein-Uhlenbeck process for the purpose of optimal control
Explicitly retained as tractable baseline despite the abstract noting heavy-tailed innovations.
standard math The reduced inventory-funding control problem admits a unique viscosity solution recoverable via monotone finite differences
Standard assumption for the numerical HJB scheme described.

pith-pipeline@v0.9.0 · 5462 in / 1327 out tokens · 60195 ms · 2026-05-08T03:17:54.713845+00:00 · methodology

discussion (0)

Reference graph

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