The Caribbean is still open, despite a slew of painful hurricanes in recent weeks, according to Carnival Corporation (CCL - Get Report) CEO Arnold Donald.

"The Caribbean is open for business - I have 20 ships in the Caribbean right now," Donald said in an interview with TheStreet. "People are having a great time."

Donald said Carnival ships are going to over 40 ports in the Caribbean and every port in Mexico is in working order. 

He expects the five damaged ports with heavy cruise activity to be back up in running "really soon."

Shares of Carnival are up some 24% since the start of the year. 

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