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- Following the Abel et. al. (2007), for simplicity, I also assume that a portfolio manager continuously rebalances the portfolio to maintain ...xed the proportion of assets invested in stocks. In this case, the portfolio return then follows a geometric Brownian motion; dR (tj; tj + s) R (tj; tj + s) = r + 0 ( R) ds + 0 p dZ: To solve the consumer's problem, I divide the problem in four steps: the consumption choice within two consecutive observation periods; the choice of riskless asset and the share invested in stocks; and two ...nal steps that uncover the value function and the optimal observational frequency.
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- If he enters the stock market, she pays Kd and her value function is: V W+ 0 = V (W0 (1 Kd)) = ( ) (W0 (1 Kd))1 ( ) = 1 e ! h (1 ) (1 ) i e 5 ! = B @ 2 (1 ) (1 ) (! ) C A where: ! = (1 ) rL ( ) r + ( R)0 1 ( R) > rL = (1 ) ( ) > 0 1. How large Kd has to be to drive agents out of the domestic market, if this is the only available risky asset, as in Abel et al. (2007)? I identify the parameters of their model by a subscript d to distinguish from the parameters of the open economy model. For this case, Kd has to be such that equals the value function of consumers that invest and those who don't invest in stocks, that is, comparing (3) to (7): V W+ 0 = V (W0 (1 Kd)) = d ( ) (W0 (1 Kd))1 = g = ! W1 d ( ) (W0 (1 Kd))1 = ! W1 1 = 1 e ! d h (1 ) (1 ) i e d d 5 (1 Kd)1 Kd = 1 1 e ! d h (1 ) (1 ) i e d d Kd = 1 B @ 1 e ! d h (1 ) (1 ) i e d d C A where d = 1 ( d r) d ( ) r + 1 ( d r)2 d ! > rL d = (1 ) d ( ) :
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