Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 30L / a / Solution

In discounted terms, an arbitrage is a portfolio with zero initial value whose terminal payoff is nonnegative in every state and strictly positive with positive probability. A risk-neutral measure is a probability measure equivalent to the physical measure under which every discounted asset price is a martingale. The one-period fundamental theorem of asset pricing says that a finite one-period market is arbitrage-free exactly when it has a risk-neutral measure.

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