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.
Probabilistic numerics expands numerical tasks with black box methods.
The paper solves complex swing option pricing equations with numerical methods.
Efficient numerical method for time-fractional Black-Scholes model.
New method solves elliptic equations on manifolds without grids.
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition and Poisson's equation with mixed boundary conditions. The principal advantage o…
Paper approximates fractional harmonic maps with numerical methods.
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
The paper extends a method for numerical conformal mappings to surfaces using Laplace-Beltrami equations.
Twelve numerical methods for Poisson geometry concepts.
Improved MLMC method for robust and efficient probability and density estimation.
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation …
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legend…
This paper tackles Bayesian system identification with probabilistic numerical methods.
Improved method for numerical conformal mappings on complex domains.
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
New method models dewetting of anisotropic particles using numerical techniques.
Neural ODEs' performance varies with numerical method, requiring adaptive step size control.
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approxi…
Numerically locating the critical points of non-convex surfaces is a long-standing problem central to many fields. Recently, the loss surfaces of deep neural networks have been explored to gain insight into outstanding questions in optimization, generalization, and network architecture design. However, the degree to wh…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…
Deep learning solves high-dimensional PDEs efficiently.
Space mapping speeds up shape optimization for PDEs.
We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic dif…
Improved numerical solution for BSDEs with reduced boundary errors.
Paper solves convertible bond valuation using finite elements with penalty method.
New method smooths integrands for efficient option pricing.
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In…
FBSJNN solves PIDEs and FBSDEJs with deep learning, offering theoretical and numerical efficiency.
Deep learning method improves numerical approximation of FBSDEs with jumps.
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
Fenrir uses probabilistic numerics to simplify solving initial value problems.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
End-to-end solution for recognizing handwritten numerals, avoiding traditional preprocessing steps.
Parallel-in-time solver reduces ODE simulation time from linear to logarithmic.
New method calculates cut locus on surfaces without boundary.
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly dete…
A new framework improves tensor completion accuracy by considering numerical priors.
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant connections on algebroids. This has fundamental consequences for the theory of numeri…
PNDMs accelerate DDPMs by treating them as differential equations on manifolds.
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.
We propose a robust and stable lattice method which permits to obtain very accurate American option prices in presence of CIR stochastic interest rate without any numerical restriction on its parameters. Numerical results show the reliability and the accuracy of the proposed method.
In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The fi…
We consider the problem of numerical approximation for forward-backward stochastic differential equations with drivers of quadratic growth (qgFBSDE). To illustrate the significance of qgFBSDE, we discuss a problem of cross hedging of an insurance related financial derivative using correlated assets. For the convergence…
Study numerical methods for singular FBSDEs with degenerate forward component.
NCG methods improve shape optimization efficiency.