= Solution
Let $Y$ be a martingale deflator for the original arbitrage-free market. Part b shows that
$$
\pi_t^HY_t+\sum_{s=1}^t\xi_s^HY_s
$$
is a local martingale. Thus $Y$ also deflates the gains of the added asset whose price and dividend are $(\pi^H,\xi^H)$. It already deflates the original $n$ assets, so it is a martingale deflator for the enlarged market. The <fundamental theorem of asset pricing> implies that the enlarged market has no arbitrage. This expresses the fact that adding a dynamically replicated asset cannot create an arbitrage.
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