Formal solutions represent series expansions that, while not necessarily convergent in the classical sense, satisfy the governing differential equations term by term. This concept has become ...

The main aim of this paper is to develop some basic theories of neutral stochastic functional differential equations (NSFDEs). Firstly, we establish a local existenceuniqueness theorem under the local ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

The classical results on the instability of the solutions of stochastic differential equations are extended in two directions: the coefficients are allowed to depend on the paths of the solutions, and ...

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 ...

In this paper, we consider the numerical valuation of swing options in electricity markets based on a two-factor model. These kinds of contracts are modeled as path dependent options with multiple ...