Deep learning and American options via free boundary framework

@article{Nwankwo2022DeepLA,
  title={Deep learning and American options via free boundary framework},
  author={Chinonso Nwankwo and Nneka Umeorah and Tony Ware and Weizhong Dai},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.11803}
}
We propose a deep learning method for solving the American options model with a free boundary feature. To extract the free boundary known as the early exercise boundary from our proposed method, we introduce the Landau transformation. For efficient implementation of our proposed method, we further construct a dual solution framework consisting of a novel auxiliary function and free boundary equations. The auxiliary function is formulated to include the feed forward deep neural network (DNN… 
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References

SHOWING 1-10 OF 68 REFERENCES

DeepXDE: A Deep Learning Library for Solving Differential Equations

An overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation, and a new residual-based adaptive refinement (RAR) method to improve the training efficiency of PINNs.

Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions

This work proposes a deep neural network framework for computing prices and deltas of American options in high dimensions, and introduces the least squares residual of the associated backward stochastic differential equation as the loss function.

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

This two part treatise introduces physics informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations and demonstrates how these networks can be used to infer solutions topartial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

DGM: A deep learning algorithm for solving partial differential equations

Selection dynamics for deep neural networks

A predictor-corrector scheme based on the ADI method for pricing American puts with stochastic volatility

MgNet: A unified framework of multigrid and convolutional neural network

A unified model, known as MgNet, is developed that simultaneously recovers some convolutional neural networks for image classification and multigrid methods for solving discretized partial differential equations (PDEs) and modified CNN models (with fewer weights and hyperparameters) are developed.

Neural Optimal Stopping Boundary

A method based on deep neural networks and empirical risk minimization and relaxed stopping rules based on fuzzy boundaries is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping.

Adam: A Method for Stochastic Optimization

This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
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