The Radner Model

• Traders can trade $L$ physical commodities in date 0 and in each time-1 state $s\in S$ spot market, and J assets.
• Asset $j$ is a promise to pay to its holder $a_s^j$ units of the good 1 in state $s$. The asset return matrix is the $|S|\times J$ matrix $A$, with rows $A_s$.
• The vector of state-contingent returns from portfolio $z\in\R^J$ is $Az$.
• The set of feasible portfolios is unbounded. $z_j \lt 0$ is a sale/short position on the numeraire payouts; $z_j\gt 0$ is a purchase/long position on the numeraire payouts.

Prices in the Radner model are spot prices $(p_0,\ldots,p_S)\in\Rlsp$ and asset prices $q\in \R^J$.