Boundary-safe PINNs extension: application to non-linear parabolic PDEs in counterparty credit risk
From MaRDI portal
Publication:6157931
DOI10.1016/j.cam.2022.115041arXiv2210.02175MaRDI QIDQ6157931
José A. García-Rodríguez, Joel P. Villarino, Álvaro Leitao
Publication date: 22 June 2023
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.02175
Artificial neural networks and deep learning (68T07) Credit risk (91G40) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)
Cites Work
- Unnamed Item
- Unnamed Item
- Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
- On the limited memory BFGS method for large scale optimization
- The numerical solution of linear ordinary differential equations by feedforward neural networks
- Nonlinear valuation under credit, funding, and margins: existence, uniqueness, invariance, and disentanglement
- PDE models and numerical methods for total value adjustment in European and American options with counterparty risk
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
- Optimally weighted loss functions for solving PDEs with neural networks
- Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
- Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Numerical methods to solve PDE models for pricing business companies in different regimes and implementation in GPUs
- Total value adjustment for a stochastic volatility model. A comparison with the Black-Scholes model
- A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
- A Theory of the Term Structure of Interest Rates
- ARBITRAGE-FREE VALUATION OF BILATERAL COUNTERPARTY RISK FOR INTEREST-RATE PRODUCTS: IMPACT OF VOLATILITIES AND CORRELATIONS
- Neural‐network‐based approximations for solving partial differential equations
- Optimization Methods for Large-Scale Machine Learning
- Solving high-dimensional partial differential equations using deep learning
- Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models
- Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
- Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs
- On a Neural Network to Extract Implied Information from American Options
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Cross Currency Valuation and Hedging in the Multiple Curve Framework
- BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART II: CVA
- Pricing Multi-Asset Options with Sparse Grids and Fourth Order Finite Differences
- A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
- Affine multiple yield curve models
- ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS
- ADI finite difference schemes for option pricing in the Heston model with correlation