Danish oil and shipping group A.P. Moller-Maersk
The company's shares rose over 6 percent as analysts said Mc-Kinney Moller's death could lead to a stock split or demergers.
Mc-Kinney Moller, born on July 13 in 1913, died at the age of 98, having made his last public appearance at the group's annual general meeting last Thursday.
As the traditional main attraction at the AGM, Moller spoke briefly to shareholders and signed autographs but looked frail as he joked there were too few female photographers present.
An analyst said the group, founded in 1904, could now face change.
It could be a stock split or a demerger of for instance Danske Bank
Moller-Maersk owns a 20 percent stake in Danske Bank as well as an interest in Dansk Supermarked Group, its website shows.
Maersk Mc-Kinney Moller, son and grandson of the founders of the A.P. Moller-Maersk group, Arnold Peter Moller and his father, Peter Maersk Moller, took over the leadership of the group when his father died in 1965.
He handed over the daily management of the group to Jess Soderberg in 1993, and the chairmanship to Michael Pram Rasmussen in 2003. Soderberg was replaced by Carlsberg Chief Executive Nils Smedegaard Andersen in 2007, while Rasmussen remains chairman.
Moller, however, remained active in the decision making and activities of the group, frequently going to the Copenhagen headquarters and travelling around the world to represent Denmark's largest privately owned enterprise himself.
A 2.5 billion crowns Moller donation resulted in a new Copenhagen opera house in January 2005.
The Maersk group owns the container shipping company Maersk Line, and is also involved in oil and gas exploration, mainly in the North Sea, but also in many other parts of the world, as well as supermarket chains, industrial firms, shipyards and a container terminal operator.
The group employs about 117,000 people in 130 countries.
Moller, born in Copenhagen in 1913 to an Irish-American mother, was known for only rarely giving interviews.
Moller married childhood girlfriend Emma in 1940 and together they raised three daughters.
Shares in A.P. Moller-Maersk initially traded up over 6 percent following the announcement, but were up 3.0 percent at 42.520 Danish crowns per share at 0958 GMT, against a 1.3 percent rise in the Copenhagen stock exchange's benchmark index <.OMXC20>.
(Reporting by Mette Fraende; Editing by Helen Massy-Beresford)