To build the stock exchange, Tropico first needs to hire an Economic Minister. Once built, the stock exchange will hire up to 5 college-educated men to become stock brokers.
Once the exchange has at least one broker, foreign investment proposals will start to occasionally appear. In these proposals, you'll get to pick one of three different choices for foreign investments, where investors from different global powers offer to pay for the construction of a building on your island and pay you monthly rent in exchange for keeping all the income from the building itself.
You have little control over private buildings. Both the wages for private workplaces and the rental rates for private housing are set by their owners. In addition, you're unable to buy upgrades for private factories and, depending on the requirements of the owner, you might not be able to change the building's work mode either.
If a private building fails to turn a profit for too long, the investors may go bankrupt, demolishing their building and ceasing to pay their rent. To avoid this, make sure private workplaces are adequately supplied with resources and workers. On islands that offer Free Housing to all, it can be very difficult for private housing to make a profit. Unless the island is overpopulated or the type of housing being offered is better than the housing everyone gets for free, it's likely that the investors will go bankrupt before tenants choose to move in.