arXiv preprints from January 1, 2026 through September 11, 2026 — 05:37:13 EST
Algebraic concordance of knots can be understood from the perspective of Seifert matrices, Blanchfield forms, and homology surgery. We initiate a systematic study of algebraic concordance for links from each of these viewpoints. The present article is concerned with algebraic concordance from the perspective of homology surgery and...
Influence matrices encode the action exerted on local subsystems by the rest of an extended quantum many-body system during their evolution. Thus, knowledge of the influence matrix facilitates computationally efficient simulations of local dynamics. Here we propose a new systematic approach to generating quantum circuits with complex...
Singular Value Decomposition (SVD) underlies matrix factorisation tasks across computational imaging, with medical applications increasingly demanding real-time processing. Yet SVD algorithms are inherently sequential, constraining real-time GPU throughput and limit online deployment in clinical pipelines. This study introduces...
We prove a series of new results in Hamiltonian dynamics on a general closed symplectic manifold $(M, ω)$, including: 1. If $M$ admits a Hamiltonian diffeomorphism which is either a pseudo-rotation or has finite order, then $M$ is geometrically uniruled. This resolves a variant of Problem 24 in McDuff--Salamon's list, which predicts...
We prove Pólya's conjectured lower bound for the Neumann counting function of every Euclidean ball. If $d\ge2$, $R>0$, and $E\ge0$, then \begin{equation*} N_{B_R^d}^{<}(E) \ge \frac{ω_d}{(2π)^d}|B_R^d|E^{d/2} = \frac{(R\sqrt E)^d}{2^dΓ(\frac d2+1)^2}. \end{equation*} The radial boundary condition in dimensions $d\ge3$ is a Dini...
An antichain is a family of rectangles in which no member contains another. Given a family $\mathcal{E}$ of rectangles, let $h_{\mathcal{E}}$ be the sum of the indicator functions of its members. We show that there exist constants $c, C > 0$ such that for every sparse antichain $\mathcal{E}$ of dyadic rectangles in $\mathbb{R}^2$ one...
Multi-warehouse inventory allocation is typically formulated as a mixed-integer programming (MIP) problem, yet no single formulation consistently matches heterogeneous instance-level regimes induced by demand concentration, inventory imbalance, replenishment scale, service constraints, and forecast volatility. We study this issue as...
We establish necessary and sufficient conditions for the uniform boundedness of the multi-parameter singular exponential sum $$ \sum_{|t_1|\le N_1,\dots,|t_k|\le N_k} \frac{e^{2πi P(t_1,\dots,t_k)}}{t_1\cdots t_k}, $$ where $P:\mathbb{Z}^k\to\mathbb{R}$ is a polynomial of the form $ P(t)=\sum_{\mathfrak{m}\in Λ} c_{\mathfrak{m}}\,...
In this work, we develop a weak-form version of Extended Dynamic Mode Decomposition that we call WEDMD. We establish a number of analytic results about the method and show explicitly how the weak form is able to mitigate the impacts of noise in linear stochastic differential equations. In nonlinear systems, we likewise show how the...
We develop an analytic Fourier cosine (COS) method for the valuation of compound options. By deriving closed-form expressions for the cosine coefficients at all compound stages, the proposed method eliminates the need for numerical quadrature in intermediate exercise stages while retaining the convergence properties of the underlying...
Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models...
A finite panel of option quotes with bid-ask spreads generally does not point-identify either the risk-neutral probability of breaching a specified threshold or the expected shortfall below that threshold conditional on a breach. Sharp marginal bounds characterize each quantity in isolation but not their jointly attainable...
Hedging a derivative position under transaction costs and market frictions requires a trading rule that adapts to changing conditions. Deep hedging trains a neural policy for this task but policy training does not determine whether a trading desk can afford to run the policy. We apply robust hedging valuation adjustment (HVA) as a...
Automated code generation is becoming an important tool in quantitative finance, where large language models can generate option pricing implementations directly from mathematical model specifications. Validating such implementations, however, requires considerably more than conventional software testing: numerical pricing methods...
This paper proposes a GARCH-type volatility model in which level-and-slope updates of a latent power-law kernel generate state-dependent decay of past shocks within a two-dimensional Markov state. We derive a joint Foster--Lyapunov condition and establish positive Harris recurrence and uniqueness of the invariant distribution....
Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known...
The standard method to price European calls on a discrete dividend-paying stock is to subtract the present value of the dividends from the initial stock price in the Black-Scholes formula. However, when there are dividends after maturity, this is inconsistent with the model. Within the escrowed dividend model, we highlight an...
We present a distinctive approach to parameterizing the risk neutral distribution. Using parsimonious and interpretable parameters, the model provides direct and localized control over the shape of the implied volatility curve. It captures a wide variety of shapes, including those with local concavity. Empirical results demonstrate...
Estimating the covariance structure of financial assets typically relies on historical returns, making risk models dependent on noisy and asset-specific time series. We propose the Characteristic-Driven Dynamic Factor Model (CD-DFM), a non-linear latent factor model that instead constructs a representation of the asset cross-section...
In the insurance industry, Asset and Liability Management (ALM) models are key tools for numerous applications, including Solvency Capital Requirement (SCR) computation and asset allocation optimization. However, their use often entails a significant computational cost, especially when a large number of sensitivities or stressed...
As in Bouchard et al. (2010) and Bouchard and Nutz (2014), we study a utility maximization problem with expectation constraint. We first consider a uniformly elliptic case in which the endogenous state boundary associated with the constraint in expectation is proved to be smooth. This allows one to derive a proper Dirichlet condition...
In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid...
The Arrow-Pratt approximation is one of the cornerstones of expected utility theory, providing the classical local approximation of certainty equivalents and risk premia in terms of absolute risk aversion. Despite its widespread use, its mathematical scope and relationship to higher-order risk preferences remain only partially...
This paper introduces a compact reformulation of a modular end-to-end neural network for global minimum-variance portfolio optimization that decouples model complexity from both look-back window length and universe size. A five-parameter hyperbolic weighted moving average combined with a saturating exponential replaces the original...
We construct the Settlement Modernisation Index, a panel dataset of 809 reform events across 24 advanced economies between 1993 and 2024, decomposed into three economic channels and three adoption phases. We document an S-curve in inside money elasticity with two interior turning points at SMI = 0.27 and 0.93, separating a liberation...