Why do closed end mutual funds list at a price that is different from the total value of assets in the fund?

For open end funds the share price * the total shares outstanding = the value of the funds holdings, but closed end funds do not keep that relationship intact. In essence, I can invest a dollar in a closed end fund which gives me a claim on $1.10 worth of the funds assets. How is that possible?

You are correct - this is unique to closed end funds AND is a situation that is watched by closed end fund traders - the fund can trade at a premium or discount to the net value of the fund, and some traders will trade the fund based on this dispartity as compared to its norm. For instance the fund normally trades at a 5% premium and it is currently at a 5% discount which is also the low discount of the year - buy the fund for a return to its normal premium.

Why? Unlike an open end fund that doesn't trade - it closes each day at the fund's net value AND can increase-decrease in size based on cash inflows-outflow. A closed end fund is just like a stock in that it is listed on an exchange AND for a given number of shares outstanding - then traders 'move' the price of the fund [stock] based on perceived change in value of the assets in the fund.

All funds trade at either a "Premium" or a "Discount" according to expectations.

In other businesses, it's called "Goodwill."

Even though past performance is not necessarily indicative of future performance, if a fund has been doing well and getting huge inflows of money, it trades at a premium. The losers have outflows, and trades a discount.

Because they are close-end. This is what close-end means; share price is determined by supply and demand, the value of net assets is only a footnote, since there is no obligation by the manager to redeem shares at that value. In addition, some closed-end funds invest in assets with limited liquidity (such as loans), for which there are no published prices, so they are carried at cost.