6Stochastic integrals

6.1 Informal definition of the Itô and Stratonovich integrals

The Black–Scholes model (3.4) is a particular case of a stochastic differential equation, but we are going to study in this book the more general case of stochastic differential equations (SDEs) in a time interval images (images) of the form


where images and images are real functions with domain images and images (initial condition) is a r.v. independent of the Wiener process images. The initial condition can, in particular, be deterministic, i.e. assume a constant real value images (in which case we may say that the r.v. is degenerate and assumes the ...

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