Related papers: Error Analysis of Deep PDE Solvers for Option Pric…
In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow…
Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
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…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge. Conventional methods, such as finite difference methods, are unable to solve high-dimensional PDEs due to the curse-of-dimensionality. A…
Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into…
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…
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…
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…
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…
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the…
Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and…
The discontinuous Petrov Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan introduced in their first paper has been widely used for problems in computational mechanics. In this investigation, we propose the DPG method for option…
The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…