The lognormal distribution, on which Example 2.3.10 is based, has an interesting property. If we have the

Question:

The lognormal on which Example 2.3.10 is based, has an interesting property. If we have the pdf

then Exercise 2.35 shows that all moments exist and sire finite. However, this distribution does not have a moment generating function, that is,

does not exist. Prove this.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...