题目
题目
单项选择题

Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 𝑐 𝑡 − 𝛼 2 𝑐 𝑡 2 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?

选项
A.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 + 1 𝑐 𝑡 ) − 𝛼 𝑥 𝑡 + 1 ]
B.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 𝑐 𝑡 + 1 𝑐 𝑡 𝑥 𝑡 + 1 ]
C.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝛼 𝑐 𝑡 2 ) 𝑥 𝑡 + 1 ]
D.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 + 1 2 𝛼 ) 𝑥 𝑡 + 1 ]
E.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 1 − 𝛼 𝑐 𝑡 + 1 1 − 𝛼 𝑐 𝑡 ) 𝑥 𝑡 + 1 ]
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思路分析
We start by outlining what the question is asking in plain terms: the investor chooses how many shares θ to buy in period t given the utility structure u(c_t) = c_t − α/2 c_t^2 and the consideration of future payoffs x_{t+1} = p_{t+1} + d_{t+1}. The goal is to derive the expression for the asset price p_t as a function of tomorrow’s payoffs, using the intertemporal optimization and the given utility form. Option A (the first choice): p_t = E_t [ β ( (1 − α c_t + 1/(1 − α c_t)) x_{t+1} + 1 ) ] - This option places the price p_t inside an expectation of a future payoff x_{t+1}, scaled by β and modified by a factor that involves α and c_t inside the parentheses, plus a constant term. The presence of (1 − α c_t) and a reciprocal term 1/(1 − α c_t) indicates an attempt to capture how marginal utility and the curvature parameter α interact with current consumption c_t to affect the pricing kernel. Conceptually......Login to view full explanation

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Consider an investor who lives 2 periods (t and t+1). She has income et in the first period and et+1 in the second period. The investor buys θ shares of an asset at price pt in the first period, and receives an uncertain payoff xt+1=pt+1+dt+1 in the second period. Her investment decision is thus described by the following maximization problem: max θ[u(ct)+β𝔼t(u(ct+1))]. Assuming that the utility function is u(ct)=ct− α 2 c 2 t what is the equation for the price of the asset in period t as a function of tomorrow’s payoffs?

Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 1 2 ( 𝑐 𝑡 − 𝛼 ) 2 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?

Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 𝑐 𝑡 𝛼 𝛼 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?

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