題組內容

6. (35%) Let wT denote the terminal wealth of a uni-dollar investment after T periods. Consider two possible cumulative distribution functions (CDFs) for wT as follows.
646716618a848.jpgwhere N(μ, σ2) represents the normal distribution with the mean to be u and the variance to be σ2. For any utility function U'(•) ≥ 0, the expected utility under F or G is
 646716bf2a37f.jpg

Last，Φ(c)≡646717235c860.jpgdx is the CDF for the standard normal distribution.  where M is a positive constant, and the expected utility under F is

6.3 (20%) Consider a utility function 646717e8950c8.jpg

where M is a positive constant, and the expected utility under F is

646718f05cb4b.jpg

6.3.1 (5%) Prove that0 <I < MΦ6467192322446.jpg