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如何理解这个等式右边第二个取极限的式子等于0？
我看了john cochrane那本asset pricing 的课后答案解释这个问题，还是没看懂，请达人求解。
附上答案的注释
The last term is not automatically zero. For example, if
greater growth will lead to such a term. It also has an interesting economic interpretation. Even
if there are no dividends, if the last term is present, it means the price today is driven entirely
by the expectation that someone else will pay a higher price tomorrow. People think they see
this behavior in “speculative bubbles” and some models of money work this way.
The absence of the last term is a Þrst order condition for optimization of an infinitely-lived
consumer. If
and increase utility. This lowers ct, increases ct+j , until the condition is filled.
If markets are complete — if he can also buy and sell claims to the individual dividends — then he
can do even more. For example, if pt >, then he can sell the asset, buy claims to each dividend,
pay the dividend stream of the asset with the claims, and make a sure, instant profit. He does
not have to wait forever. (Advocates of bubbles point out that you have to wait a long time to
eat the dividend stream, but they often forget the opportunities for immediate arbitrage that a
bubble can induce. The plausibility of bubbles relies on incomplete markets.)
Bubble type solutions show up often in models with overlapping generations, no bequest motive,
and incomplete markets. The OG gets rid of the individual Þrst order condition that removes
bubbles, and the incomplete markets gets rid of the arbitrage opportunity. The possibility of
bubbles figures in the evaluation of volatility tests.
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