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Deep BSDE solver in TensorFlow !
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# Deep BSDE Solver in TensorFlow (2.0)

## Training

```python main.py --config_path=configs/hjb_lq_d100.json
```

Command-line flags:

• `config_path`
: Config path corresponding to the partial differential equation (PDE) to solve. There are seven PDEs implemented so far. See Problems section below.
• `exp_name`
: Name of numerical experiment, prefix of logging and output.
• `log_dir`
: Directory to write logging and output array.

## Problems

`equation.py`
and
`config.py`
now support the following problems:

Three examples in ref : *

`HJBLQ`
: Hamilton-Jacobi-Bellman (HJB) equation. *
`AllenCahn`
: Allen-Cahn equation with a cubic nonlinearity. *
`PricingDefaultRisk`
: Nonlinear Black-Scholes equation with default risk in consideration.

Four examples in ref : *

`PricingDiffRate`
: Nonlinear Black-Scholes equation for the pricing of European financial derivatives with different interest rates for borrowing and lending. *
`BurgersType`
: Multidimensional Burgers-type PDEs with explicit solution. *
`QuadraticGradient`
: An example PDE with quadratically growing derivatives and an explicit solution. *
`ReactionDiffusion`
: Time-dependent reaction-diffusion-type example PDE with oscillating explicit solutions.

New problems can be added very easily. Inherit the class

`equation`
in
`equation.py`
and define the new problem. Note that the generator function and terminal function should be TensorFlow operations while the sample function can be python operation. A proper config is needed as well.

## Dependencies

Note: an old version of the deep BSDE solver compatiable with TensorFlow 1.12 and Python 2 can be found in the commit 9d4e332.

## Reference

 Han, J., Jentzen, A., and E, W. Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning, Proceedings of the National Academy of Sciences, 115(34), 8505-8510 (2018). [journal] [arXiv]
 E, W., Han, J., and Jentzen, A. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Communications in Mathematics and Statistics, 5, 349–380 (2017). [journal] [arXiv]