= Solution
The current price of one unit of certain future <consumption> is the sum of the <Arrow state prices>, namely $0.9$. A unit-price <risk-free asset> yielding gross return $R$ must satisfy $0.9R=1$. Hence
$$
\boxed{R=\frac{10}{9}.}
$$
Normalize the <Arrow state prices> by their sum, or multiply them by $R$, to obtain the <risk-neutral probabilities>:
$$
\boxed{Q=(\tfrac19,\tfrac29,\tfrac13,\tfrac13).}
$$
They are positive and sum to one. Any terminal payoff $Y$ has current price $\sum_sp_sY_s=R^{-1}\mathbb E_QY$. In particular any asset with current price one has $\mathbb E_Q r_i=R$. These pricing probabilities need not equal the physical probabilities governing the investor's <utility>.
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