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.
Galerkin method outperforms graph-based methods in spectral decompositions.
Study methods to recover unknown processes in PDEs from data.
Neural Galerkin schemes use active learning to solve high-dimensional equations.
New boundary treatment improves accuracy for complex PDEs.
Paper explores solving HJB equations using neural networks.
New ARIMA framework improves forecast accuracy for economic and financial time series.
Review and compare model order reduction methods for process engineering.
One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneous…
A new method uses neural networks to improve POD-Galerkin models for complex systems.
New methods for clustering graphs using spectral analysis.
Deep Galerkin Method estimates value function for mean-field control problem.
Paper establishes convergence rates for learning elliptic pseudo-differential operators.
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to uni…
Develops numerical methods for PDEs on hypergraphs and networks.
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…
New method learns diffusion transition density for Bayesian inference.
Proves regularity for quasilinear elliptic equations in metric spaces.
This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \[ dR_t= (θ+σα(R_t, t))R_t dt +σR_t dB_t \] with an initial value , where and are constants, and the mean correction function $α:\mathbb{R}\times[0,\infty)\to α(x,t)\…
This paper presents four different ways of looking at the well-known Least Squares Temporal Differences (LSTD) algorithm for computing the value function of a Markov Reward Process, each of them leading to different insights: the operator-theory approach via the Galerkin method, the statistical approach via instrumenta…
DGNet solves complex dynamical systems with neural networks and constraints.
This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.
Paper solves investment strategy optimization with deep learning.
Deep learning method proves convergence for high-dimensional PDEs.
A machine learning approach to compute Black-Scholes prices with uncertain volatility.
A new model captures forward curve dynamics with stochastic volatility.
Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.
New method uses randomized sparse neural networks to solve time-dependent PDEs more accurately and efficiently.
In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre p…
We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in . These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives…
Book introduces deep learning methods with math, theory, and applications.
We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly …
This research analyzes deep PDE solvers for option pricing accuracy.
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that the…
Paper characterizes optimal learning trajectories for high-dimensional nonlinear models.
Two neural network methods solve the master equation for MFGs.
Research improves pricing of multidimensional American options using neural networks.
Optimizes trading in CFMMs and exchanges using deep learning.
New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is mo…
CoLoRA models predict PDE solutions quickly and accurately with minimal data.
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportun…
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou…
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…