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.
Neural Galerkin schemes use active learning to solve high-dimensional equations.
Galerkin method outperforms graph-based methods in spectral decompositions.
Deep Galerkin Method estimates value function for mean-field control problem.
A new method uses neural networks to improve POD-Galerkin models for complex systems.
Deep learning method proves convergence for high-dimensional PDEs.
Review and compare model order reduction methods for process engineering.
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…
Paper explores solving HJB equations using neural networks.
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…
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…
Study methods to recover unknown processes in PDEs from data.
Research improves pricing of multidimensional American options using neural networks.
Paper solves investment strategy optimization with deep learning.
New ARIMA framework improves forecast accuracy for economic and financial time series.
Paper establishes convergence rates for learning elliptic pseudo-differential operators.
New boundary treatment improves accuracy for complex PDEs.
Develops numerical methods for PDEs on hypergraphs and networks.
Optimizes trading in CFMMs and exchanges using deep learning.
Book introduces deep learning methods with math, theory, and applications.
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…
This research analyzes deep PDE solvers for option pricing accuracy.
New method uses randomized sparse neural networks to solve time-dependent PDEs more accurately and efficiently.
Proves regularity for quasilinear elliptic equations in metric spaces.
New deep learning method for option pricing in jump-diffusion models.
New method learns diffusion transition density for Bayesian inference.
In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal execution, mean field games, etc. The main idea behind DGM is to represent the unknown…
A machine learning approach to compute Black-Scholes prices with uncertain volatility.
Study optimal semi-static hedging for illiquid markets using dynamic cash and static quoted derivatives.
New methods for clustering graphs using spectral analysis.
Two neural network methods solve the master equation for MFGs.
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…
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)\…
DGNet solves complex dynamical systems with neural networks and constraints.
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…
A new model captures forward curve dynamics with stochastic volatility.
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 …
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…
With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Fin…
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…
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 …
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neur…
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…
This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.
Paper uses autoencoders for efficient reduced-order modeling of eigenvalue problems.
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…
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…
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
CoLoRA models predict PDE solutions quickly and accurately with minimal data.