The evidence supports target-dependent inductive bias, not a universal winner, in target-dependent inductive bias, and the evidence supports target-dependent inductive bias, not a universal winner in inductive bias.
Abstract
Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark exposes simulator-truth densities for latent evaluation, while a chronological NIFTY benchmark tests only held-out market prices. A two-component lognormal mixture has the lowest aggregate price, $L^1$, Wasserstein, and fixed-tail errors on the synthetic benchmark. Learned operators retain narrower strengths: DeepONet reduces 1% quantile and variance error by 39.0% and 34.6% relative to the mixture, and a quote transformer reduces $L^1$ by 16.4% on the structurally misspecified Merton family. A numerical conditioning analysis explains why these rankings can differ: after enforcing mass and forward constraints, 95 of 126 pricing directions are numerically null, and two densities separated by $L^1 = 0.061$ produce identical prices on the covered strikes. On 524 held-out NIFTY calls, validation-selected test-time adaptation reduces DeepONet RMSE by 28.3%, but per-expiry mixture and SVI fits remain much more accurate. The evidence supports target-dependent inductive bias, not a universal winner.
In incomplete markets, no-arbitrage (NFLVR) guarantees the existence, not the uniqueness, of an equivalent local martingale measure (ELMM): unhedgeable risks (jumps, stochastic volatility) admit a whole family of equivalent measures, and asset dynamics alone cannot pin down the one the market selects. We characterize the identifiability of $Q$ from option data and propose a measure that is identifiable from data yet prices any claim consistently. The key boundary is an ``identification wall'': European options identify only the terminal marginal, while out-of-sample tails and path/joint structure require instruments matched to the priced risk (variance or higher-moment swaps, path-dependent claims). Within this view, minimum-relative-entropy weighted Monte Carlo (WMC) is the optimal baseline for the marginal; we generalize it to a full path-space measure change parameterized by a neural network on physical scenarios---XiNet---which learns $\xi=\mathrm{d}\mathbb{Q}/\mathrm{d}\mathbb{P}$ directly from 8 model-free path features, with option prices as a soft constraint. On European (marginal) pricing XiNet matches but does not surpass WMC, and both are bound by the identification wall out-of-sample. On path-dependent claims the picture reverses: calibrated on the same European surface, per-marginal methods fail structurally (an ATM forward-start is mispriced by $\sim+100\%$), whereas XiNet's single self-consistent measure keeps the bias to $+0.3\%$, beating maximum-entropy WMC ($-24\%$), because $\xi=f_\theta(\text{path features})$ captures joint structure Europeans cannot constrain. Identification is thus risk-specific, and XiNet is a single measure that absorbs available instruments and prices all claims consistently.
Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-level distribution-valued characteristics can instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed from Qwen3-Embedding-8B news representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reported frozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.
Algorithmic trading now represents a market exceeding $20 billion, where even marginal gains in signal robustness can translate into economically significant returns. Existing evaluations of equity prediction models do not explicitly target regime robustness during hyperparameter selection. Five model classes are trained on daily observations from approximately 300 large-cap US equities over eleven years, with Bayesian optimisation configured to target trading performance across three statistically different market regimes. Regime-robust hyperparameter selection is associated with out-of-sample generalisation, as signal precision remains above the random baseline across all four quarters of the test period, and portfolio performance slowly degrades under simulated input noise before collapsing beyond a defined threshold. No individual tabular deep learning architecture outperforms gradient-boosted trees, but combining XGBoost and TabNet using rank aggregation produces a Hybrid ensemble with an annualised return of 51.26%, a Sharpe ratio of 2.44, and a statistically significant CAPM alpha of 0.423 (p = 0.011). A near-zero beta indicates this outperformance is driven by stock selection, not market exposure. Alternative data plays a secondary role once technical and fundamental features are accounted for, as well as contributing more strongly on the short side than the long, and varies by model class. An interactive application makes these results explorable in real time, with live data integration the remaining step toward practical deployment.
We generate infinite binary exchangeable sequences by sequential comparison of data points against a latent benchmark. Assuming a prior distribution of the benchmark rank \(R_0\) within an unobserved group, we set up the Bayesian machinery that determines the posterior distribution of the running rank \(R_n\) in purely combinatorial terms. This yields an explicitly computable predictive probability of winning against the benchmark. The normalised running rank converges to a latent strength variable \(X\) with polynomial density, possibly Beta-tilted. Some min-max tournaments lead to particularly simple multiplicative formulae for predictive probabilities related to priors that generalise the Topp--Leone distribution; for that class we analyse the asymptotics of the associated fixed-\(n\) up-down Markov chains. The limiting diffusion has the classical Wright--Fisher variance but a nonlinear drift expressed explicitly via the prior density of the benchmark. Mixtures of Beta densities are classical objects in the theory of exchangeable sequences. The contribution of the present work is the combinatorial rank-based updating mechanism and the resulting explicit predictive laws for sequential testing against an unknown benchmark.
Robust portfolio rules that reconstruct confidence sets after learning need not preserve the evaluator obtained by prior-by-prior Bayesian transport. In the Gaussian model, this discrepancy is summarized by natural-coordinate displacement: inherited transport preserves it whereas fresh reconstruction can replace it. We price evaluator replacement and trace the resulting optimized curvature through endogenous research. Optimized robust value represents protocol regret as a functional Bregman divergence, while a within-vintage rectangular Gaussian benchmark with constant absolute risk aversion (CARA) yields a stopped recalibration tax. In a versioned model-release economy, validated history propagates through a strictly causal network and a same-cycle share of current optimized marginal value feeds back into research supply. The capacity-constrained equilibrium reduces to a scalar equation with protocol-indexed gain \(\mathfrak g_I^P=\lambda\beta_{R,I}(W_R^P)''\). Purely causal validation cannot create a same-cycle unit mode; provenance changes criticality through optimized curvature. For a scalar primitive supplier-score shock \(z\) in direction \(h_I\) and financial outcome \(\mathcal O\), sensitivity factors as \(\omega_{\mathcal O,h,I}/(1-\mathfrak g_I^P)\). Conditional on a smooth equilibrium state and active cell, completion-time information sharply bounds this multiplier when all compatible timing laws are subcritical; no finite uniform bound exists when the timing set reaches the pole.
We present in this article a non-parametric value-at-risk (VaR+CVaR) algorithm that remains accurate for an arbitrarily large number of underlying positions. The algorithm solves the two inherent problems of VaR estimation. First, past history is not directly applicable to the future, but all predictions of the future are based on the past. Second, VaR estimation is equivalent to modeling a single corner of a high-dimensional space (the corner where all bets lose simultaneously). The algorithm only uses mathematical methods that strictly do not degrade in accuracy at high-dimensions. Historical data are then directly incorporated with all high-dimensional relationships present, without manipulation. We test the algorithm with an ensemble of 500 portfolios with random positions across 49 distinct liquid futures of different expiries (VIX, equity indexes, gov. bonds, rates, energy, metals, livestock, agriculture, and softs). All VaR estimations are performed strictly blind to the future. The median portfolio rate of loss exceeding the 99% confidence daily VaR estimate is between $1.0\pm0.1$% depending on algorithm input parameters. 68% of portfolios have a rate of loss exceeding 99% VaR between $1.0\pm0.3$%, and 95% of portfolios between $1.0\pm0.5$%.
Siyuan Sun· Journal of Risk· 0 citations
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