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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 211 / 2 / a / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2022 iii Paper 211 2 a
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The discrete-time fundamental theorem of asset pricing supplies a strictly positive martingale deflator Y. Since the maturity-T bond pays one unit at T, its deflated price is a martingale:
Yt​PtT​=E(YT​∣Ft​).
(1)
Division by Yt​>0 gives the formula.

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