微观金融技术与方法优秀课件

X1 = +10 X2 = -1
E(X) = (0.5) (10) + (0.5) (-1) = 4.50
if you play this game many times, you will be a big winner How much would you pay to play this game:
And this solves the paradox
1.3 投资者行为
个人决策准则
一、确定性环境：选择与偏好 在确定性环境下分析个人的理性决策行为，需要权衡
不同抉择好坏优劣的价值尺度。建立在选择行为之上的偏 好关系（preference relation）可以用一种两维的关系 （binary relation）表述出来。
perhaps as much as a $4.50 But of course the answer depends upon your preference to risk
Fair Gambles
if the cost to play these gambles
= expected value of the outcome
U'(X) > 0
MU positive
U"(X) < 0
diminishing MU
E(U(W)) = αi U(Xi) = αi ln(Xi) = 1.39 <
an individual would pay an amount up to 1.39 units of utility to play this gamble
ixi
12i 1
2i
i1
Explaining the St. Petersburg Paradox
this paradox arises because individuals do not make decisions based on purely on their wealth, but rather on the utility of their expected wealth
1.2 一些常用的投资决策准则
一、 收益最大准则
收益最大准则应用于完全没有风险的情况下。由此法 则，只需选择收益率最高的投资机会即可。经济学中的生 产者理论和价值理论广泛使用这一准则。
在金融经济学中，不确定环境下，收益最大准则不再 适用。
二、 最大期望收益准则
使用投资收益的期望值作为各种投资方案的比较，是 收益最大准则在不确定情形下的推广。
then the gamble is said to be actuarially fair
Common empirical findings:
1. individuals may agree to flip a coin for small amounts of money, but usually refuse to bet large sums of money
定义（偏好关系）：投资选择集 C上的偏好关系是指具有完
备性、自反性和传递性的一个二维关系。
a) 完备性（completeness）
对于任何 x, yC ,要么 x y 要么 y x ；
2. people will pay small amounts of money to play actuarially unfair games (for example, cost = $1, but E(X) > 1) - but will avoid paying a lot
Why do these empirical findings occur?
if you play this game many times, it is unlikely that you will win or lose anything
Example 2
Gamble (X) flip of a coin if heads, you receive $10: if tails, you pay $1:
圣彼得堡悖论（Saint Petersburg paradox）
Gamble (X): A coin is flipped until a head appears, You receive $2n , where n is the flip on
which the head occurred
if we can show that the marginal utility of wealth declines as we get more wealth, then we can show that the expected value of a game is finite
Assume U(X) = ln(X),
states: prob:
X1 = $2 X2 = $4
X3 = $8 ...
Xn = $2n
α1 = 1/2 α2 = 1/4 α3 = 1/8 ...
αn = 1/2n
E(X) =
Paradox: no one would pay an actuarially fair price to play this game (no one would even pay close to the fair price)
是否期望收益最大准则就是一 (X) flip of a coin
if heads, you receive $1: X1 = +1
if tails, you pay $1:
X2 = -1
E(X) = (0.5) (1) + (0.5) (-1) = 0
微观金融技术与方法
第一章 偏好表示与风险厌恶
1.1 引言
期望效用理论全面考虑了投资收益的风险和收益的概率分布 情况，是研究不确定环境下个体消费和投资决策的主要工具。
风险厌恶型投资者的投资行为 本章主要建立期望效用理论的基础，和资产定价理论的微观
经济基础。
➢ 对待风险的态度 ➢ 风险厌恶的度量 ➢ 两基金货币分离