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About the article
Published Online: 2013-08-13
Published in Print: 2014-02-01
See also Blume and Easley (1992, 1993).
It is possible that rational arbitrageurs are risk-averse, and noise traders are risk-loving. Therefore, as pointed out by one of the referees, the assumption of homogeneous risk-aversion is unreasonable in the current paper. By relaxing the assumptions of homogeneous degrees of risk-aversion and homogeneous expected conditional variance, Chiarella and He (2002) test the robustness of the results of Brock and Hommes (1998). They also investigate the effects of different memory lengths on the dynamics. Chiarella and He (2002) found that Brock and Hommes’s (1998) results are robust to this generalization. However, they do point out that the resulting dynamic behavior with this generalization is considerably enriched and exhibits some significant differences. Thus, how to incorporate the heterogeneous beliefs and risk in a simple asset pricing model with social interactions in order to investigate the resulting herd behavior and bubbles in financial markets will be an important extension of the current paper.
The belief type of the noise trader used in this paper is equivalent to the term “trend chaser” with a belief bias in Brock and Hommes (1998). Notice that the term “noise trader” may have a different scope than a “trend chaser” with a belief bias in Brock and Hommes (1998). See for example, DeLong et al. (1990).
The belief type of arbitrageurs used in this paper is equivalent to the term “contrarian” with a belief bias in Brock and Hommes (1998). Notice that the term “arbitrageurs” may be used differently in the finance literature. For example, in Hull (2011), “arbitrageurs” is used to denote the traders who are involved in “locking in a risk-less profit by simultaneously entering into transactions in two or more markets.”
Here, S(‧) represents proportional spillover-type social interactions; see Brock and Durlauf (2001a,b).
See Brock and Durlauf (2001a,b) and Anderson, Palma and Thisse (1996) for a derivation.
Notice that the sufficient condition for |km*|<R is k<R.
Friedman (1953, p. 175) argues, “People who argue that speculation is generally destabilizing seldom realize that this is largely equivalent to saying that speculators lose money, since speculation can be destabilizing in general only if speculators on average sell when currency is low and buy when it is high.”
Blume and Easley (1992, 1993) find that the most fit behavior in the financial market is that which maximizes the expected growth rate of wealth share accumulation.