“If we have some relative calm for some period of time, I see us fully recovering our yields in a matter of a few years,” Arison said.

And he intends to be at the helm when that happens. At 63, Arison, who also owns the Miami Heat, said retirement is not a near-term prospect.

“I have no hobbies,” he said, other than the championship basketball team. “So I don’t know what I’d do if I didn’t do this...This is all I’ve done for 40-plus years, and done it 24-7.”

Still, he said he has discussions with Carnival’s board regularly about a succession plan in case something unexpected were to happen to him.

“We have an outstanding group of executives around the globe, many of whom are capable candidates to take over if something happens to me,” he said. “The board is very much aware of what I would do in the circumstance of me being hit by a truck...I don’t think it’s appropriate to discuss it because there’s more than one executive who would be interested in competing for that.”

Frank, 71, who has been with the company since 1989, said he wants to stick around as long as Arison and the board want him to. Guidelines for corporate governance say that directors won’t be nominated to the board after they turn 75, but provides that such a nomination could happen “under special circumstances.”

“I think the business is something in some small way I helped to create with Micky,” he said. “I think of it more as my business, and I think of it more as an owner than a manager...It is my life in many, many ways and I enjoy it.”

Arison said he’s told Frank to see how he feels in a year or two — for awhile now.

“We’ve been doing that for five or six years,” he said.

But Frank said he’s probably more excited about the company’s future now than he was even five years ago.

Despite the downs in 2012, the company remained profitable, bringing in net income of $1.3 billion — the lowest annual profit since 2003 — on $15.4 billion in revenues. That followed the itinerary upheaval associated with the Arab Spring in 2011 and, of course, the recession in the United States that sent profits and revenues tumbling in 2009.

“What’s been strange in the cruise space is it’s been a longer recovery time from the recession than most of us would have thought originally to try to recapture those 2008 yields,” said Sharon Zackfia, an analyst with William Blair & Co., a Chicago-based investment firm. “There have been several years of difficult events that the cruise lines have had to digest: swine flu, more significant was the Arab Spring, last year Concordia. It’s just been almost two steps forward, one step back.”

But Arison pointed out that Carnival has remained profitable throughout all of those twists. And the company has other reasons for optimism. In June, the 3,600-passenger Royal Princess debuts for the Princess Cruises brand, featuring a soaring atrium, new dining options and a glass-bottomed enclosed walkway jutting out 28 feet beyond the deck.

Royal Princess is just one of two ships Carnival Corp. is expecting this year; the other, for the German AIDA brand, arrives in March. The company has only two ships per year on order through 2016; Carnival has been saying for the past several years that it wants only two to three new ships a year.