Stochastic differential equations (SDEs) provide a powerful framework for modelling systems where randomness plays a crucial role. Estimation methods for SDEs seek to infer underlying parameters that ...

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 ...

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 ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Differential equations don’t have to feel like an endless maze of formulas. With the right mix of tech tools, real-world context, and problem-solving strategies, they can become a skill you actually ...

Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

In his doctoral thesis, Michael Roop develops numerical methods that allow finding physically reliable approximate solutions ...

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 ...