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Found 12 papers, 4 papers with code
Quasi-Monte Carlo for Efficient Fourier Pricing of Multi-Asset Options
Nonetheless, the applicability of RQMC on the unbounded domain, $\mathbb{R}^d$, requires a domain transformation to $[0, 1]^d$, which may result in singularities of the transformed integrand at the corners of the hypercube, and deteriorate the rate of convergence of RQMC.
Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features
We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks.
Scalable method for Bayesian experimental design without integrating over posterior distribution
A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design.
Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in Lévy Models
First, we smooth the Fourier integrand via an optimized choice of the damping parameters based on a proposed optimization rule.
Nonlinear Isometric Manifold Learning for Injective Normalizing Flows
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution.
Numerical Smoothing with Hierarchical Adaptive Sparse Grids and Quasi-Monte Carlo Methods for Efficient Option Pricing
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may critically depend on the regularity of the integrand.
On the equivalence of different adaptive batch size selection strategies for stochastic gradient descent methods
In this study, we demonstrate that the norm test and inner product/orthogonality test presented in \cite{Bol18} are equivalent in terms of the convergence rates associated with Stochastic Gradient Descent (SGD) methods if $\epsilon^2=\theta^2+\nu^2$ with specific choices of $\theta$ and $\nu$.
Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation
The updated mean of the CMF matches that of the posterior, obtained by applying Bayes' rule on the filter's forecast distribution.
Wind Field Reconstruction with Adaptive Random Fourier Features
In particular, random Fourier features is compared to a set of benchmark methods including Kriging and Inverse distance weighting.
A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean--Vlasov equations
By employing a system of interacting stochastic particles as an approximation of the McKean--Vlasov equation and utilizing classical stochastic analysis tools, namely It\^o's formula and Kolmogorov--Chentsov continuity theorem, we prove the existence and uniqueness of strong solutions for a broad class of McKean--Vlasov equations.
Probability Numerical Analysis Numerical Analysis 65C05, 62P05
Weak error rates for option pricing under linear rough volatility
We prove rate $H + 1/2$ for the weak convergence of the Euler method for the rough Stein-Stein model, which treats the volatility as a linear function of the driving fractional Brownian motion, and, surprisingly, we prove rate one for the case of quadratic payoff functions.
Pricing American Options by Exercise Rate Optimization
Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates.
