Structure of GEI-Excess Demand
Finance is built on the assumption of complete rationality. The absence of arbitrage based on the utility maximization principle is then the most fundamental insight of this theory. Therefore it is important to know that, as we have shown in Chapter 2, the model is logically consistent, i.e. that under some mild assumptions on the characteristics of the model competitive equilibria exist. In this section we show that without any further assumptions than those made in Chapter 1 the no-arbitrage condition is actually all we can conclude from the model. That is to say, any arbitrage free vector of asset prices is the equilibrium price vector of some economy. Following the argument of Harrison and Kreps  one can show that this result is trivial when the state space is finite and no restrictions on the trading volume are required. A single agent economy in which the agent has a risk neutral expected utility function with beliefs equal to the martingale measure generates the given asset prices. However in a single agent economy there is no trade—an obvious contradiction to what we observe. In this chapter we show that even with an arbitrary preassigned trading volume the no-arbitrage condition is all we can expect. Even worse we will show that in some economies there may be arbitrarily many ways of having a no-arbitrage condition that is compatible with the economic fundamentals because the number of equilibria is not restricted by the rationality hypothesis. In particular this shows that without knowledge of the characteristics of the economy finance has no empirical implications! Only if auxiliary assumptions like small or constant absolute risk aversion are made we get definite conclusions from the rationality hypothesis. If as it is nowadays put forward by many empirical studies (see for example Campbell , Hirshleifer  and De Bondt  for surveys) there are serious asset price “anomalies” then it is unclear whether those refute the fundamental assumption of rationality or rather the auxiliary assumptions made to make the model well determined.
KeywordsAsset Price Excess Demand Martingale Measure Price Vector Incomplete Market
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