Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

In this paper, we consider the valuation of European and path-dependent options in foreign exchange markets when the currency exchange rate evolves according to the Heston model combined with the ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues. The trajectory of a storm ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...