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###### 日期：2019-05-17 10:09

CFRM 415 - Introduction to Financial Markets

Assignment 5

Due: May 17, 2019 - 11:59 pm

Question 1: i) Suppose an investor has initial wealth W0 and has the opportunity for an investment such

that the end-of-period wealth is W = W0 + H. If the investor uses exponential utiliy, show that WC W0

does not depend on W0.

ii) Suppose an investor has initial wealth W0 and has the opportunity for an investment such that the

end-of-period wealth is W = HW0. If the investor uses power utility show that WC

W0

does not depend on

W0.

Question 2: Let W, a random variable, represent the amount of future wealth held by an investor, and

let u1 and u2 be two different utility functions. The certainty equivalent of W under u1 is denoted W

and the certainty equivalent of W under u2 is denoted W. Using the definition of certainty equivalent

and the definition of equivalent utility functions, show that if u1 ～ u2 then W

You may assume

u1 and u2 are strictly increasing.

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