Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 50

In Chapter 2 we discussed both systems of ODEs and scalar ODEs. The focus was mainly concerned with notation, the structure of ODEs and finite difference schemes to approximate them. We implicitly assumed that the solution of the corresponding initial value problem existed in an otherwise unspecified time interval and that the solution was unique. These assumptions constitute a huge leap of faith. In this chapter we discuss existence and uniqueness results for ODEs and stochastic differential equation (SDEs). We also introduce several important numerical schemes and code in C++ and Python.