We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “small-noise expansion”
DSM on manifolds removes singularities and computes small-noise expansions.
problem DSM on manifolds with singular noise.
method Rao-Blackwellized score matching, nearest-point projection, intrinsic Riemannian score.
result Canonical target equals intrinsic Riemannian score up to a small correction.
Density expansions for hypoelliptic diffusions are revisited. In particular, we are interested in density expansions of the projection , at time , with . Global conditions are found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptot…
New method improves nonlinear filtering accuracy with reduced computation.
problem Complex nonlinear filtering with small system noise.
method Asymptotic expansion with ordinary differential equations and Edgeworth-type correction.
result Significantly lower computational cost with improved accuracy.
In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions , at fixed time and projected to their first coordinates, in the small noise regime. Global conditions were found which replace th…
New method analyzes volatility models for option prices, especially in rough volatility.
problem Analyzing option prices in rough volatility models.
method Introducing a new methodology to analyze stochastic volatility models, focusing on asymptotics and numerics.
result Detailed expansion and numerical evidence for implied volatility in rough volatility models.
New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.
problem Comparative analysis of regularization norms in ill-posed problems.
method Small noise analysis framework for Tikhonov and RKHS regularizations.
result Optimal convergence rates achieved with adaptive fractional RKHS, but hyper-parameters decay too fast.
Quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low dimensional Markovian representation, which greatly simplifies their numerical implementation. We present a qualitative study of the solutions of the quasi-Gaussian log-normal HJM model. Using a small…
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
Study recovers Riemannian quantities from noisy data densities.
problem Recovering geometric structure from noisy data on submanifolds.
method Derive uniform small-noise expansions of noisy density and its derivatives; construct estimators for tangent spaces, intrinsic dimension, and second fundamental form.
result Fundamental Riemannian quantities identifiable from density derivatives.
We present a novel methodology based on a Taylor expansion of the network output for obtaining analytical expressions for the expected value of the network weights and output under stochastic training. Using these analytical expressions the effects of the hyperparameters and the noise variance of the optimization algor…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so…
Large learning rates prevent memorization in denoising score matching.
problem Memorization of training data in diffusion-based generative models.
method Investigating the role of large learning rates in the small-noise regime, proving that they prevent convergence to the empirical optimal score.
result Large learning rates prevent memorization by making it impossible for the learned score to be arbitrarily close to the empirical optimal score.
Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.
problem Large deviations for hypoelliptic diffusion measures on sub-Riemannian manifolds.
method Rough path theory and manifold-valued Malliavin calculus.
result Proved a large deviation principle for pinned hypoelliptic diffusion measures.
The one-dimensional SDE with non Lipschitz diffusion coefficient is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving instances of this equation, based on a careful i…
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary informatio…
Study large deviations in fractional volatility models with non-Gaussian volatility.
problem Large deviations in fractional volatility models with non-Gaussian volatility.
method Established a small-noise large deviation principle for log-price.
result Logarithmic call price asymptotics for large strikes in a special case.
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
Deep learning solves dynamic programming with recursive utility.
problem Challenges in solving high-dimensional discrete-time dynamic programming problems with recursive utility.
method Certainty Equivalent Learning (CEL) algorithm that learns certainty-equivalent value directly with neural networks.
result Accurate value and policy approximations in high-dimensional problems, comparable to VFI in some cases.
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughnessmath.PR
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
Reduces learning periodic neural networks to lattice problems, proving hardness under cryptographic assumptions.
problem Learning single periodic neurons in noisy environments.
method Reduction to worst-case lattice problems, using LLL algorithm.
result Polynomial-time algorithms for learning these functions are hard under cryptographic assumptions.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with small noise parameters. We prove that this approximation can be understood math…
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough vola…
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
problem Understanding and improving the generalization of neural networks.
method Introducing weight expansion and showing that dropout leads to it.
result Dropout increases the generalization of neural networks by expanding the weight space.
We present ErasureHead, a new approach for distributed gradient descent (GD) that mitigates system delays by employing approximate gradient coding. Gradient coded distributed GD uses redundancy to exactly recover the gradient at each iteration from a subset of compute nodes. ErasureHead instead uses approximate gradien…
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra and a Mathematica implementation to compute .
result Derivation of large-color expansion from universal invariant.
Functional Expansionsq-fin.MF
This work explores functional expansions to handle path dependence in various fields.
problem Path dependence and infinite-dimensional problems in non-Markovian systems.
method Generalizes Wiener series and functional Taylor expansion to handle static and dynamic functionals.
result Elegant separation of functionals from future trajectories in dynamic cases.
In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e. the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function. We study higher genus correctio…
On the third coefficient in the TYCZ-expansion of the epsilon function of Kaehler-Einstein manifoldsmath.DG
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
problem Understanding Kaehler-Einstein metrics and their epsilon functions.
method Computes the third coefficient in the TYCZ-expansion of the epsilon function.
result Discovers the vanishing of the third coefficient's significance.
We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data. This paper is concerned with the consistency of optimization-based techniques for such problems, in the limit where the labels have small noise and the underlying unl…
Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.
problem Asymptotic expansion of heat trace for thermoelastic Dirichlet-to-Neumann map.
method Provided a method to obtain all coefficients of the asymptotic expansion.
result Explicitly gave the first two coefficients involving volume and total mean curvature of the boundary.
The paper proposes and proves asymptotic expansions for quantum invariants.
problem Quantum invariants and their expansions under varying metrics.
method Asymptotic expansion conjectures for relative Reshetikhin-Turaev, Turaev-Viro invariants and quantum 6j-symbols.
result Proved asymptotic expansions for special cases, showing geometric dependence on metrics.
Motivated by marginals-mimicking results for Itô processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely if $X_{\cdot}=(Y_\cd…
New method models portfolios with leptokurtic risk factors using Gram-Charlier expansions.
problem Modeling portfolios with excess kurtosis.
method GC-like expansions of the hyperbolic-secant law to account for leptokurtosis.
result Portfolio distribution with risk factors modeled as GC-like expansions of the HS law.
Develops AMITE for analyzing neural network nonlinearities.
problem Addressing difficulties in verification, explainability, and security in neural network analysis.
method Analytically modified integral transform expansion (AMITE) for neural network nonlinearities.
result First to provide six mutually exclusive desired expansion properties.
We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.