Related papers: Financial option valuation by unsupervised learnin…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized…

Option pricing often requires solving partial differential equations (PDEs). Although deep learning-based PDE solvers have recently emerged as quick solutions to this problem, their empirical and quantitative accuracy remain not well…

This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our…

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…

A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Lohne & Rudloff (2014) is compared to a special case of the algorithms for…

We characterize the price of a European option on several assets for a very risk averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic…

We present a method for solving linear and nonlinear PDEs based on the variable projection (VarPro) framework and artificial neural networks (ANN). For linear PDEs, enforcing the boundary/initial value problem on the collocation points…

Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that…

The explainable artificial intelligence is used to analyze the stochastic Fredholm integral equations (SFIEs) and stochastic deep neural networks (SDNNs). The neural operator-based stochastic fixed point framework is used to develop SDNNs.…

This paper proposes the Exact Terminal Condition Neural Network (ETCNN), a deep learning framework for accurately pricing American options by solving the Black-Scholes-Merton (BSM) equations. The ETCNN incorporates carefully designed…

We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or…

Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with…

In a global derivatives market with notional values in the hundreds of trillions of dollars, the accuracy and efficiency of pricing models are of fundamental importance, with direct implications for risk management, capital allocation, and…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

Artificial neural networks (ANNs) have gained a well-deserved popularity among machine learning tools upon their recent successful applications in image- and sound processing and classification problems. ANNs have also been applied for…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schr\"odinger equation, as a result we get…