本次英国代写主要为金融经济学相关的限时测试
ECN349 Summer exam paper with solutions
A 部分（回答 Q1 和 Q2；回答 Q3 或 Q4） 50 分
Q1。回答问题的以下部分。
a) 简述什么是 Arrow-Pratt 绝对风险系数
厌恶（ARA）和相对风险厌恶（RRA）。 (5 分)
b）计算并解释对数的ARA和RRA值
效用函数�（�）=log𝑎�，其中a是一个正参数而x
>0.注意x可以理解为与每个可能的结果相关联
给定选择，或者给定每种可能的财富水平
选择的结果。 (5 分)
建议答案：
a) 绝对风险厌恶的 Arrow-Pratt 系数 (ARA, 2-
维度）描述效用函数的局部曲率。给定一个
单调递增效用函数（指示不可满足的代理
假设），度量的负值对应于风险-
寻求行为和积极价值观来避免风险行为。
ARA系数越大，规避风险越大（或风险越小）
爱）一个人处于x的水平。
𝐴�𝐴(�) = −�′′
(�)/�′
(�)
相对风险厌恶的 Arrow-Pratt 系数（RRA，2-
维）是另一种局部风险规避度量，它描述了
个人对比例风险的态度。
随着财富的增加，RRA 不变/减少/增加意味着
个人愿意承担风险的财富比例
随着财富的增加保持不变/增加/减少。
��𝐴（�）= −�𝑢′′
(�)
𝑢’（�）
Section A (answer both Q1 and Q2; answer either Q3 or Q4) 50 marks
Q1. Answer the following parts of the question.
a) Briefly explain what Arrow-Pratt coefficients of absolute risk
aversion (ARA) and relative risk aversion (RRA) are. (5 marks)
b) Calculate and interpret the ARA and RRA values for the logarithmic
utility function �(�) = log𝑎 �, where a is a positive parameter and x
>0. Note x can be understood as each possible outcome associated
with a given choice, or the level of wealth given each possible
outcome of a choice. (5 marks)
Suggested answer:
a) Arrow-Pratt coefficient of absolute risk aversion (ARA, 2-
dimentional) describes local curvature of a utility function. Given a
monotone increasing utility function (indicating non-satiable agents
assumption), negative values of the measure correspond to risk-
seeking behaviour and positive values to risk-avoiding behaviour.
The greater the ARA coefficient, the more risk averse (or less risk
loving) an individual is at the level of x.
𝐴�𝐴(�) = −�′′
(�)/�′
(�)
Arrow-Pratt coefficient of Relative risk aversion (RRA, 2-
dimensional) is another local risk aversion measure that describes
an individual’s attitude toward proportional risks.
Constant/decreasing/increasing RRA with increasing wealth means
the proportion of wealth that an individual is willing to put at risk
remains constant/increases/decreases as wealth increases.
��𝐴(�) = −�𝑢′′
(�)
𝑢′(�)