C.Zhou Journal of Economic Dynamics and Control 22 (1998)1027-1051 1037 emb,Um and Wo for agent b can be analyzed symmetrically.Although II is the same for everybody in the stock market,different people may have different perceptions of it.This difference will lead to different portfolio demands between agents and therefore to interesting trading dynamics. 5.Differential information equilibrium Using the information extraction method introduced above,we now solve for a market equilibrium under differential information. 5.1.Trading strategy and portfolio choice Let Wa be agent a's wealth and be the vector of agent a's stockholdings. Similar to the corresponding perfect information model,the optimization problem is max E[exp(-Wa+1)], (44) subject to Wa.t+1 =(1 r)W at Qarena.t Qana.t+1, (45) where all symbols are defined as before. It follows directly that the optimal stock portfolio of agent a is Qa=Endena Ena[-rp hgaYa-(1+r)P], (46) Where En.a=E[Una+1na+1]. One can solve agent b's optimization problem symmetrically and gets Qo =En.ben.b =Emb[-rp hgoYo-(1 +r)], (47) where is agent b's stock portfolio and En.=E,[Umb.+1Um+]is the variance-covariance matrix of mb. The portfolio demand equations,Eqs.(46)and(47),show that rational eco- nomic agents partially diversify their portfolios in light of their private informa- tion.For example,agent a holds both stocks even though he or she is better informed about stock 1 and less informed about stock 2.Agent a's demand forePb , €Pb and ¼b for agent b can be analyzed symmetrically. Although P is the same for everybody in the stock market, different people may have different perceptions of it. This difference will lead to different portfolio demands between agents and therefore to interesting trading dynamics. 5. Differential information equilibrium Using the information extraction method introduced above, we now solve for a market equilibrium under differential information. 5.1. Trading strategy and portfolio choice Let ¼a be agent a’s wealth and Qa be the vector of agent a’s stockholdings. Similar to the corresponding perfect information model, the optimization problem is max Qa Et [!exp(!¼a,t`1 )], (44) subject to ¼a,t`1 "(1#r)¼at#Q@ atePa,t #Q@ at€Pa,t`1 , (45) where all symbols are defined as before. It follows directly that the optimal stock portfolio of agent a is Qa "RP~1a ePa "R~1 Pa [!rp#hu a Ya !(1#r)PI], (46) where RP,a "Et [€Pa,t`1 €@ Pa,t`1 ]. One can solve agent b’s optimization problem symmetrically and gets Qb "RP~1 ,b eP,b , "R~1 Pb [!rp#hu b Yb !(1#r)PI], (47) where Qb is agent b’s stock portfolio and RP,b "Et [€Pb,t`1 €@ Pb,t`1 ] is the variance—covariance matrix of €Pb . The portfolio demand equations, Eqs. (46) and (47), show that rational eco￾nomic agents partially diversify their portfolios in light of their private informa￾tion. For example, agent a holds both stocks even though he or she is better informed about stock 1 and less informed about stock 2. Agent a’s demand for C. Zhou / Journal of Economic Dynamics and Control 22 (1998) 1027—1051 1037