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 ...

Differential-algebraic equations (DAEs) serve as a critical framework in mathematical modelling by integrating both differential and algebraic components to represent systems with inherent constraints ...

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 ...

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 ...

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

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 ...

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 ...

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation ...