A <one-period martingale deflator> is a pair $Y_0>0$, $Y_1>0$ such that
$$
\mathbb E[Y_1P_1]=Y_0P_0.
$$
If $Y^0,Y^1$ are deflators and $\varepsilon_0,\varepsilon_1>0$, their positive linear combination is strictly positive and
$$
\mathbb E[(\varepsilon_0Y_1^0+\varepsilon_1Y_1^1)P_1]
=(\varepsilon_0Y_0^0+\varepsilon_1Y_0^1)P_0.
$$
It is therefore another martingale deflator.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 211 / 2 / a / Solution

For price vectors $P_0,P_1$, a one-period martingale deflator is a pair $Y_0>0$, $Y_1>0$ satisfying $\mathbb E[Y_1P_1]=Y_0P_0$ componentwise.


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