Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 29K / a

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- Solution a

Solution

Let

V_{t}

denote wealth measured in units of the strictly positive numéraire. A predictable self-financing portfolio is an arbitrage if

V_{0} = 0, V_{T} \geq 0 P -almost surely, P (V_{T} > 0) > 0.

Equivalently, one may permit

V_{0} \leq 0

provided one of the two gains is strict.

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