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Market Conditions under Frictions and without Dynamic Spanning

In this paper we study the conditions for the absence of arbitrage, single agent’s optimality, and equilibrium in a market under frictions and with more sources of uncertainty than tradable assets. In other words, we analyze a stateprice deflator, i.e., a deflator with the property that the deflated prices of tradable assets are martingales, in the presence of frictions and incompleteness. A unique state-price deflator may exist only on projected markets. It is shown that if the market conditions hold for the projected markets, they hold also for the initial market.