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.
New approximations for Asian basket spread options using stochastic Taylor expansions.
We propose \emph{Taylorized training} as an initiative towards better understanding neural network training at finite width. Taylorized training involves training the -th order Taylor expansion of the neural network at initialization, and is a principled extension of linearized training---a recently proposed theory …
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely used as building blocks for deep learning algorithms. This paper provides the fi…
New sampling scheme improves ML accuracy in physics simulations.
New learning algorithm for real analytic functions without gradient descent.
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…
This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods …
Approximates option prices in Barndorff-Nielsen and Shephard models using Taylor expansion.
Proposes a Taylor framework to unify and analyze attribution methods.
SOAR improves deep networks' robustness against adversarial examples.
In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by Lévy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to devel…
The paper modifies asset pricing models using Taylor series expansions and market-based averages.
Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce "multivariable" manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. …
This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the trader's view on valuation. This is followed by Taylor series approximation for …
Unified framework for analyzing machine learning model attributions.
New samplers reduce NFEs for diffusion models.
Paper improves kernel approximations for better statistical learning.
Paper proposes a closed-form formula for geometric Istanbul call options.
Agents learn state ambiguity from non-linear sensor data using Gaussian approximations.
Paper proves existence of a CMC hypertorus in 4D sphere using numerical methods.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
In this paper we study the pricing of exchange options when underlying assets have stochastic volatility and stochastic correlation. An approximation using a closed-form approximation based on a Taylor expansion of the conditional price is proposed. Numerical results are illustrated for exchanges between WTI and Brent …
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
Paper proves existence of solutions for complex surface diffusion equation.
Expanding the rough Heston model in
We study differential forms and their higher-order generalizations by interpreting them as functions on map spaces. We get a series of approximations of "generalized manifolds" (i.e. of sheaves and stacks) somewhat akin to Taylor series.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
Scannell and Sinha considered a spectral sequence to calculate the rational homotopy groups of spaces of long knots in n-dimensional Euclidean space, for n greater than or equal to 4. At the end of their paper they conjecture that when n is odd, the terms on the antidiagonal on the second page precisely give the space …
It is shown that geodesics in the space of Kähler potentials can be uniformly approximated by geodesics in the spaces of Bergman metrics. Two important tools in the proof are the Tian-Yau-Zelditch approximation theorem for Kähler potentials and the pluripotential theory of Bedford-Taylor, suitably adapted to Kähler man…
Taylor expansions improve reinforcement learning policies.
Energy distance measures feature heterogeneity in federated learning.
Study on DiTs' rates of approximation and estimation under various data assumptions.
Neural networks learn higher-order derivatives for physics problems.
This paper examines the assumptions of the derived equivalence between dropout noise injection and regularisation for logistic regression with negative log loss. We show that the approximation method is based on a divergent Taylor expansion, making, subsequent work using this approximation to compare the dropout …
This paper tackles catastrophic forgetting in neural networks by providing a unified framework for regularization-based continual learning.
Study finds Deep Taylor Decomposition is unreliable for explaining neural networks.
Derives functional Itô formula for non-anticipative maps of rough paths.
CO2 algorithm creates coresets for generic smooth divergences efficiently.
The first aperiodic monotiling, introduced by Taylor, was based on a trapezoidal prototile equipped with 14 distinct decorations. A presentation of the closely related Taylor-Socolar aperiodic monotiling is based on a hexagonal prototile equipped with 7 decorations. This paper gives decoration-free algebraic descriptio…
In the setting of exponential investors and uncertainty governed by Brownian motions we first prove the existence of an incomplete equilibrium for a general class of models. We then introduce a tractable class of exponential-quadratic models and prove that the corresponding incomplete equilibrium is characterized by a …
Although Deep Neural Networks(DNNs) have achieved successful applications in many fields, they are vulnerable to adversarial examples.Adversarial training is one of the most effective methods to improve the robustness of DNNs, and it is generally considered as solving a saddle point problem that minimizes risk and maxi…
Paper approximates XVA for European contingent claims using BSDEs and polynomial expansions.
We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process…
FFCP improves FCP's speed without sacrificing accuracy.