Sovereign countries without a stock exchange is one of those pieces of knowledge that I know has been on your mind when having a chat at the local restaurant or tavern with some of your "buds".
So, for your conversational intellect; the list is in the below link and will be part of a future version of "Trivial Pursuit", eh?
I'm sure many of these sovereigns have a "trading desk".
https://en.wikipedia.org/wiki/List_of_countries_without_a_stock_exchange