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.
We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kern…
The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions [13, 23] in the so--called G−framework…
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti…
We study first and second order conformal symmetries of the Yamabe Laplacian on a general pseudo-Riemannian manifold and of the Paneitz operator on Einstein spaces. We show that first order conformal symmetries of the Yamabe operator induce second order conformal symmetries. We show that on an Einstein space every conf…
AMAGOLD improves stochastic gradient MCMC by infrequent Metropolis-Hastings corrections.
problem Bias in stochastic gradient Hamiltonian Monte Carlo (SGHMC).
method AMAGOLD infrequently uses Metropolis-Hastings corrections to remove bias, with a fixed step size schedule.
result AMAGOLD converges to the target distribution with a fixed, rather than a diminishing, step size, and at most a constant factor slower convergence rate.
Goursat showed that in the presence of an intermediate integral, the problem of solving a second-order Monge-Ampere equation can be reduced to solving a first-order equation, in the sense that the generic solution of the first-order equation will also be a solution of the original equation. An attempt by Hermann to giv…
Nonnegative matrix factorization (NMF) has been widely used in machine learning and signal processing because of its non-subtractive, part-based property which enhances interpretability. It is often assumed that the latent dimensionality (or the number of components) is given. Despite the large amount of algorithms des…
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around …
We examine the fixed points to first-order RG flow of a non-linear sigma model with background metric, dilaton and tachyon fields. We show that on compact target spaces, the existence of fixed points with non-zero tachyon is linked to the sign of the second derivative of the tachyon potential V′′(T) (this is the anal…
This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given family. For the risk estimation problem, we compute the bias (which can also be …
The study derives generalization bounds for neural oscillators, improving their performance with regularization.
problem Quantifying the generalization capacities of neural oscillators.
method Using Rademacher complexity and squared Wasserstein-1 distances, the study derives theoretical upper PAC generalization bounds for neural oscillators.
result Theoretical bounds show polynomial growth in estimation errors with MLP size and time length, and regularization improves performance.
This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate Itô semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correc…
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a n…
Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.