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Existence of equivalent martingale measures in finite dimensional securities markets. (English) Zbl 0852.90023
Summary: Given the information structure and the number of securities, we characterize the set of all price-dividend systems for which there exist a dynamic portfolio with strictly positive value through time, and a strictly positive probability $$Q$$ such that, expressing prices and dividends in units of such portfolio, every gain process is a $$Q$$-martingale. We also weaken our characterization by showing that the existence of a trading strategy with strictly positive payoffs only is generically sufficient for the existence of an equivalent martingale measure. Finally, an example shows that our results robustly extend the current literature on the topic.

##### MSC:
 91B24 Microeconomic theory (price theory and economic markets) 91B28 Finance etc. (MSC2000)
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