Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 39 / 1 / ii / Solution

An equivalent martingale measure is a probability measure $Q$ equivalent to the objective measure $P$, meaning the two have exactly the same null events, under which the discounted stock ${\tilde{S}}_t=S_t/B_t$ is a martingale. In this one-period model the condition isThe discounted bank account is identically one. Integrability of the discounted stock is part of the martingale condition. In an augmented market the discounted price of every additional asset must satisfy the same condition.