BRUSSELS, Belgium — Belgian prosecutors said on Thursday they have closed an investigation into a €2.9 billion ($3.24 billion) capital increase in a Belgian company owned by billionaire and chief executive of LVMH Bernard Arnault.

Arnault has accepted a deal to end the case opened in 2012 against Pilinvest, a holding company in Belgium, "without any prejudicial admission of guilt on his part", prosecutors said, without offering any further details.

One of France's richest men, the luxury goods tycoon caused controversy in 2012 by requesting Belgian nationality as France prepared to introduce a 75 percent supertax. It prompted prosecutors to look into his Belgian companies.

Arnault later withdrew the request and said his frustrated efforts to acquire Belgian nationality were motivated not by tax concerns but a desire to tie up legal ownership issues so that his children would not fight over the riches he would one day leave to them.

By Alissa de Carbonnel; editor: Philip Blenkinsop and Alison Williams.