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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

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 ...