We evaluate the hedging performance of a high-order compact finite difference scheme from [4] for option pricing in Bates model. We compare the scheme's hedging performance to standard finite difference methods in different examples. We observe that the new scheme outperforms a standard, second-order central finite dif…
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.
169,051 papers · 148 categories
Trend · papers per month
48 results for “finite difference approximation”
Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space…
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…
Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.
problem Learning mappings between infinite-dimensional spaces and finite-dimensional approximations.
method Graph kernel network architecture with message passing for kernel integration.
result Competitive performance compared to state-of-the-art solvers for PDEs.
Higher finiteness properties of arithmetic approximate lattices: The Rank Theorem for number fieldsmath.GR
The paper extends a theorem to number fields without infinite places.
problem Finiteness properties of arithmetic approximate lattices.
method Geometric and homological finiteness properties for countable approximate groups.
result The finiteness length is finite and can be computed explicitly.
Paper analyzes error in stochastic approximation for discontinuous functions.
problem Estimating expected error in discontinuous stochastic approximation.
method Uses finite differences and error estimate for discontinuous functions.
result Achieves error estimate of for discontinuous stochastic representation.
Asymptotic and Finite Sample Analysis of Nonexpansive Stochastic Approximations with Markovian Noisecs.LG
This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.
problem Applying stochastic approximation to reinforcement learning settings with nonexpansive operators.
method Investigates nonexpansive stochastic approximations with Markovian noise, providing asymptotic and finite sample analysis.
result First-time proof of convergence for classical tabular average reward temporal difference learning.
Efficiently approximates higher-order derivatives for generative models.
problem Expensive computation of higher-order derivatives in generative models.
method Rewrite SM objective in terms of directional derivatives and use finite difference for efficient approximation.
result Comparable results to gradient-based methods but significantly more computationally efficient.
Improved method for estimating derivatives of discontinuous functions using stochastic algorithmic differentiation and regression.
problem High Monte-Carlo error in finite difference approximation of discontinuous functions.
method Combining stochastic algorithmic differentiation and regression to estimate derivative of expectations of discontinuous functions.
result Reduction in Monte-Carlo error through decoupling integration of Dirac delta and conditional expectation.
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
Finite-time bounds on error for linear stochastic approximation and TD learning.
problem Finite-time bounds on error for linear stochastic approximation and TD learning.
method Finite-time bounds derived using Lyapunov functions and Stein's method.
result Finite-time bounds on the moments of the error, including lower-order and higher-order moments.
Study on distributional TD learning with linear approximations for better return estimation.
problem Estimating the return distribution of a policy in reinforcement learning.
method Finite-sample analysis of distributional TD learning with linear function approximation, using the linear-categorical Bellman equation and exponential stability arguments for products of random matrices.
result Sample complexity of linear distributional TD learning matches that of classic linear TD learning, indicating similar difficulty in estimating return distribution versus its expectation.
A discrete method approximates hyperbolic curvature flow in the plane.
problem Modeling wave phenomena in solid-liquid interfaces.
method Semidiscrete finite difference method for hyperbolic curvature flow.
result Error bounds for natural discrete norms are proven.
New algorithms for approximating stochastic processes efficiently.
problem Finding accurate finite approximations for stochastic processes.
method Develops new algorithms and fast implementations for approximating stochastic processes.
result Efficient approximations for stochastic processes can be found.
New numerical method for quantile hedging in imperfect markets.
problem Quantile hedging in non-linear markets with imperfections.
method Piecewise Constant Policy Timestepping (PCPT) coupled with monotone finite difference approximation.
result Convergence of the proposed numerical scheme proved using BSDE arguments.
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
The paper analyzes discrete approximations to minimize curve length in Euclidean space.
problem Minimizing the length of curves between two sets in Euclidean space.
method Finite differences and numerical integration for discrete approximations.
result The squared length of the reconstructed curve converges to the squared minimal length with rate .
The paper uses polyhedral expansions to capture the shape of compact metric spaces.
problem Capturing the shape of compact metric spaces using finite approximations.
method Inverse sequences of polyhedra based on finite approximations of a compact metric space.
result Proves the General Principle and computes inverse persistent homology groups.
Improved TD learning with tail averaging and regularization achieves optimal convergence rates.
problem Convergence analysis of TD learning with linear function approximation.
method Tail-averaging and regularization applied to TD learning algorithm.
result Achieves optimal convergence rate in expectation and with high probability.
We analyze the Hessian spectra of large models up to 100B parameters.
problem Accurate Hessian spectra of large foundation models are difficult to obtain.
method We use shard-local finite-difference Hessian vector products and stochastic Lanczos quadrature.
result We produce the first large-scale spectral density estimates of foundation models.
Enhanced DFO using adaptive batch-based FD estimates.
problem Derivative-free optimization with imprecise gradient estimates.
method Adaptive batch-based finite difference estimation and dynamic sampling strategy.
result Algorithm achieves convergence rate similar to KW and SPSA methods.
High-order compact finite difference scheme for option pricing in stochastic volatility jump modelsq-fin.CP
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in ti…
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
Study on natural actor-critic for POMDPs with finite memory.
problem Learning in partially observed Markov decision processes with noisy observations.
method Finite actor-critic method with multi-step temporal difference learning.
result First non-asymptotic global convergence for POMDPs with function approximation.
This paper establishes lower bounds for smooth nonconvex finite-sum optimization.
problem Understanding the complexity of finding optimal solutions in nonconvex finite-sum optimization.
method Proving tight lower bounds for the complexity of finding ε-suboptimal points and ε-approximate stationary points.
result Existing algorithms achieve optimal IFO complexity up to logarithmic factors.
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement learning, its theoretical analysis has proved challenging and few guarantees on its s…
The study optimizes Gaussian process approximations for finite-rank models.
problem Posterior behavior of finite-rank approximations differs from parent GP priors.
method Locally supported basis expansions with dependent Gaussian coefficients.
result Finite-rank expansions inherit the same posterior contraction rate as parent GP priors.
The paper explores the limits of deep neural networks in approximating various function classes.
problem Characterizing the limits of deep neural networks in function approximation.
method Develops a theory relating function complexity and network complexity, using Kolmogorov complexity.
result Deep networks are optimal approximants for various function classes and provide exponential approximation accuracy.
Study numerical methods for singular FBSDEs with degenerate forward component.
problem Numerical approximation of singular fully coupled FBSDEs with degenerate forward component and non-smooth terminal condition.
method Splitting approach to treat diffusion and transport parts separately.
result The splitting method converges with rate 1/2 under structural condition.
Heavy-Tailed and Long-Range Dependent Noise in Stochastic Approximation: A Finite-Time Analysiscs.LG
Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.
problem Analyzing stochastic approximation under heavy-tailed and LRD noise.
method Noise-averaging argument to regularize impact of non-classical noise.
result Established first finite-time moment bounds for SA under heavy-tailed and LRD noise.
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an approach to scalable approximate GP regression with finite-data guarantees on th…
We develop methods to approximate derivatives for causal inference problems using data.
problem Estimating causal effects from data when distributions are not known.
method Constructive algorithm approximating Gateaux derivatives via finite differencing.
result Derives conditions for finite-difference approximations to preserve statistical benefits.
A quadrisecant of a knot is a straight line intersecting the knot at four points. If a knot has finitely many quadrisecants, one can replace each subarc between two adjacent secant points by the line segment between them to get the quadrisecant approximation of the original knot. It was conjectured that the quadrisecan…
New algorithms improve distributional TD learning with linear approximations.
problem Estimating return distributions in reinforcement learning.
method Fine-grained analysis of linear-categorical Bellman equation, variance reduction techniques.
result Tight sample complexity bounds for distributional TD learning with linear approximations.
A new method for approximating CV and bootstrap with higher-order infinitesimal jackknife.
problem Efficiently approximating cross-validation and bootstrap methods for machine learning.
method Higher-order infinitesimal jackknife (HOIJ) using Taylor series approximations and automatic differentiation.
result HOIJ provides higher-order accuracy and can be computed efficiently even in high dimensions.
Decentralized TD learning converges linearly with linear function approximation.
problem Policy evaluation in fully decentralized multi-agent reinforcement learning.
method Temporal-difference learning with linear function approximation, analyzing i.i.d. and Markovian samples.
result Local estimates converge linearly to the optimum under both i.i.d. and Markovian samples.
Temporal difference learning explained through gradient splitting, improving convergence times.
problem Learning value functions in Markov Decision Processes with linear approximations.
method Interpreting TD learning as gradient splitting and applying convergence proofs from gradient descent.
result Improved convergence times for TD learning, especially with a minor variation.
This paper proves neural networks can approximate any infinite-dimensional map with uniform guarantees.
problem Universal approximation of infinite-dimensional maps by neural networks with uniform guarantees.
method Analysis of various infinite analogues of neural networks and their approximation capabilities.
result Any continuous map can be approximated arbitrarily closely by some infinite neural networks with mild topological conditions.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
Paper tackles super-resolution of measures with machine learning techniques.
problem Approximating a finitely supported measure from its coefficients.
method Defining a distance metric, explicit expression for recuperation operator, and estimating approximation quality.
result Best possible estimates for approximation quality are shown.
The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian tail and those with monitoring throughout their lifespan is emphasized. Rates of…
Paper analyzes biased stochastic approximation with a novel multistep Lyapunov function.
problem Finite-time analysis of biased stochastic approximation algorithms.
method Developed a multistep Lyapunov function to analyze convergence and error bounds.
result First finite-time error bounds for TD- and Q-learning with linear function approximation.
New method uses adaptive sampling for optimization in uncertain conditions.
problem Optimizing functions with unknown gradients in uncertain environments.
method Adaptive sampling quasi-Newton method with finite differences and norm tests.
result Potential performance benefits of the proposed method demonstrated in preliminary experiments.
We explain how the Transference Principles from Diophantine approximation can be interpreted in terms of geometry of the locally symmetric spaces with , and how, via this dictionary, they become transparent geometric remarks and can be easily proved. Indeed, a finite family …
Variational approximations for curve flows on Riemannian manifolds.
problem Approximating solutions to curvature and elastic flow problems on Riemannian manifolds.
method Variational formulations, finite element approximations, piecewise linear elements, stability analysis.
result Derived schemes can compute rotationally symmetric self-shrinkers and geodesics.
The paper analyzes off-policy TD-learning using generalized Bellman operators and provides finite-sample bounds.
problem High variance in off-policy TD-learning due to importance sampling.
method Derives finite-sample bounds for off-policy TD-like algorithms using generalized Bellman operators.
result First-known finite-sample guarantees for several off-policy TD algorithms.
New method avoids saddle points without gradients.
problem Optimizing non-convex functions efficiently.
method Zero-order derivative-free algorithm using only function evaluations.
result Converges to second-order stationary points efficiently.
Simulation of Multidimensional Diffusions with Sticky Boundaries via Markov Chain Approximationmath.PR
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.