A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.
Philipp GrohsFabian HornungArnulf JentzenPhilippe von WurstembergerPublished in: CoRR (2018)
Keyphrases
- partial differential equations
- black scholes
- numerical methods
- solving partial differential equations
- artificial neural networks
- image denoising
- image processing
- numerical solution
- level set
- anisotropic diffusion
- numerical algorithms
- numerical scheme
- neural network
- multiscale
- finite difference method
- option pricing
- difference equations
- differential equations
- image enhancement
- energy functional
- finite difference
- computational intelligence
- fourth order
- diffusion equation
- curve evolution
- fuzzy numbers
- financial markets
- stock exchange
- genetic algorithm
- multiresolution
- denoising
- high order
- pattern recognition
- graphical models
- natural images