We state the theorem first for the special case when the stochastic process of interest is a Wiener process. This special case is sufficient for risk-neutral pricing in the Black-Scholes model.

Let be a Wiener process on the Wiener probability space . Let be a measurable process adapted to the natural filtration of the Wiener process , such that

where SE is the stochastic exponential of x with respect to W, i.e. is the solution of the integral equation

This theorem can be used to show in the Black-Scholes model the unique equilibrium price measure (or risk neutral measure) , i.e. the measure in which the fair value of a derivative is the discounted expected value, Q, is specified by