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OVERCONFIDENCE 118g parameter.The fundamental variable fis not observable.However,it sarisfies 乐=-λ(f-f)du+o,d% (2) where A>0 is the mean reversion parameter,fis the long-run mean of f o>0 is a constant volatility parameter,and Z/is a standard Brownian motion.The asset is in finite supply,and we normalize the total supply to unity. There are two sets of risk-neutral agents.The assumption of risk neu- trality not only simplifies many calculations but also serves to highlight the role of information in the model.Since our agents are risk-neutral, the dividend noise in equation(1)has no direct impact in the valuation of the asset.However,the presence of dividend noise makes it impossible to infer fperfectly from observations of the cumulative dividend process. Agents use the observations of Dand any other signals that are correlated with fto infer current fand to value the asset.In addition to the cu- mulative dividend process,all agents observe a vector of signals s4 and sthat satisfy ds fdt +odz (3) and ds "fidt +odz", (4) where Z4 and Z"are standard Brownian motions,and o >0 is the com- mon volatility of the signals.We assume that all four processes Z,Z, Z,and Z"are mutually independent. Agents in group A (B)think of s(s)as their own signal,although they can also observe s"(s4).Heterogeneous beliefs arise because each agent believes that the informativeness of his own signal is larger than its true informativeness.Agents of group A(B)believe that innovations dz4 (dz")in the signal s4(s")are correlated with the innovations dz in the fundamental process,with (0<<1)as the correlation pa- rameter.Specifically,agents in group A believe that the process for s4 is ds,=fd+o,φdZ+oN1-ΦdZ Although agents in group A perceive the correct unconditional volatility of the signal s",the correlation that they attribute to innovations causes them to overreact to signal s4.Similarly,agents in group B believe that the process for s"is ds,“=fdt+o,dZ+o,v1-中dZ On the other hand,agents in group A (B)believe (correctly)that in- Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
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