MILAN, Italy — Giorgio Armani won't be giving up control of his fashion empire, at least not while he's still on the catwalk.“While I am alive, there will be independence,” Armani, 81, told reporters Monday after his spring-summer fashion show in Milan. “Soon after, perhaps I will have prepared the ground for a type of independence that is more measured, more controlled.”Some of the biggest names in fashion are presenting succession quandaries as they enter their twilight years. Armani and Chanel designer Karl Lagerfeld are in their 80s, while Bernard Arnault, chairman of the company that owns Louis Vuitton, is 66. At stake are combined annual revenue of more than $40 billion and Europe's hold on the global market for designer handbags, shoes and other personal luxury goods.Armani, who rose to prominence dressing Richard Gere in the 1980 film American Gigolo, said last year he hasn’t made up his mind about what happens to his business after him. In May, he said a stock market listing or a foundation were possibilities, while excluding selling to a large group.The designer has no children, though his nephew and two nieces are on the board, and has previously explored deals with Hermes International SCA and Arnault’s LVMH Moet Hennessy Louis Vuitton SE. His closely held company had revenue of 2.5 billion euros ($2.8 billion) in 2014 from sales of such labels as AJ Armani Jeans and Emporio Armani. He’s also behind the Armani hotels in Milan and Dubai.“Being able to choose the light that you like in an office as much as designing an unruly or highly elegant collection, this is independence,” said Armani, who serves as owner, creative director and chief executive officer of the company he founded 40 years ago. “But you need means to maintain independence.”By: Andrew Roberts and Flavia Rotondi; editors: Matthew Boyle and Phil Serafino.