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 ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

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 ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from ...