arXiv subjects

Nam Anh Le

Publications and source records attributed to Nam Anh Le.

4 recordsLinked to original sources

arXiv2026

Finite-horizon quantile martingale posteriors: raw-urn laws and matrix-gain regression

Martingale posteriors quantify uncertainty by forward-imputing observations from one-step-ahead predictive distributions, but implementations stop after finitely many imputations. For the empirical Pólya-urn posterior of a quantile the law of the stopped state is derived. The quantile of the stopped urn measure keeps the familiar martingale tail-sum variance fraction; the deployed stochastic-approximation tracker with frozen gain $c$ does not. Its variance carries an explicit factor $G_a$ with $a=cf_0(q_τ)$, which may fall below or exceed the tail fraction, and a density-adapted gain restores calibration through a density-free inflation. Shared urn innovations yield the joint law of finitely many quantile levels. For conditional quantile regression, a smoothed martingale posterior started at the ordinary quantile-regression estimator with a full inverse-Jacobian matrix gain satisfies a process Bernstein--von Mises theorem with calibrated finite-horizon bands; scalar or diagonal gains cannot match the sandwich covariance process.

math.ST↗

arXiv2026

Decomposing Crowd Wisdom: Domain-Specific Calibration Dynamics in Prediction Markets

Prediction market prices are often read as probabilities, but this reading requires calibration. Using 353 million trades across 429,000 binary contracts on Kalshi and Polymarket, this paper measures how calibration varies with event domain, time-to-resolution and trade size. A descriptive decomposition of cell-level logistic recalibration slopes explains 87.3\% of in-sample variance on Kalshi (71.5\% out-of-sample). The most robust pattern is persistent underconfidence in political markets, where prices compress toward 50\%; it replicates on Polymarket. Large political trades on Kalshi are associated with further compression, with a calibration-slope gap of roughly one-half that survives market- and event-clustered bootstraps but is not robust on Polymarket. A Bayesian measurement-error model that propagates first-stage uncertainty agrees with these conclusions and indicates that, under conservative event-clustered standard errors, roughly half of the raw slope variation reflects estimation noise. Calibration is therefore conditional: a price's meaning depends on what, when and how much is traded.

stat.AP↗

arXiv2026

When can a posterior predictive check identify the learning rate? Exact degeneracy in Gaussian models and implications for Generalised Bayesian Inerence

Generalised Bayesian inference tempers the likelihood by a learning rate $η$ to mitigate model misspecification, and the choice of $η$ is consequential. Zafar and Nicholls (2024) proposed selecting $η$ by a posterior predictive check (PPC): one chooses the smallest $η$ at which a log-likelihood PPC $p$-value is not rejected. An exact, finite-sample analysis of this selector on the Gaussian linear model is given. With known variance and a flat prior, the PPC $p$-value equals $P(χ^2_n > \mathrm{RSS}/σ_0^2)$ for every $η$, so the selector is $η$-invariant; under variance misspecification it is two-sided non-identifying. With unknown variance and the reference prior, the $p$-value depends only on $(n,d,η)$ and not on the realised data or the data-generating process. Consequently the selector's output is fixed before any data are seen, typically collapsing to the smallest grid value, which over-tempers and inflates predictive intervals relative to held-out selection. The phenomenon is a pivotality property specific to the Gaussian scale--location family and the reference prior; it disappears under informative priors. These results delineate the selector's scope, identify a canonical class on which it cannot identify the learning rate, and motivate a cheap, data-free pre-screening diagnostic.

stat.ME↗

arXiv2026

Funding-Aware Optimal Market Making for Perpetual DEXs

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.

q-fin.MF↗