Carlyle Group on Tuesday filed documents with federal regulators to sell stock to the public, peeling away the cover on the inner financial workings at the intensely private investment giant for the first time.

The District-based financial powerhouse, which is among the world’s largest private equity firms with about $150 billion in assets under its control, filed with the U.S. Securities and Exchange Commission amid strong economic head winds that are roiling stock markets.

While the sale of stock may not happen for months, experts said, Carlyle’s filing displayed a fundamental optimism in the economy.

“Like a doctor who sees lots of patients every day, these guys have lots of touch points in terms of the economy through their portfolio companies,” said Josh Lerner, a professor at Harvard Business School who has studied private equity. “This conveys that message that whatever the short-run fluctuations, they probably don’t think [the economy] is as bad as the way that it would be portrayed on television news.”

Carlyle spokesman Chris Ullman declined to comment.

The 400-page filing did not contain anticipated numbers such as partner compensation or the amount of stock that the firm will sell. But a public offering would allow the company’s three founders — Daniel A. D’Aniello, William E. Conway Jr. and David M. Rubenstein — to eventually cash out billions.

“One of the things that is going to be fun to watch is that this [document] is going to have to be expanded,” said Colin Blaydon, director for the Center for Private Equity and Entrepreneurship at Dartmouth College’s Tuck School of Business. “It’s going to have more detail about the compensation of principal players, which makes for delicious Washington, D.C.-type gossip.”

The founders, who hold 60 percent of the company, have said they have no intention of leaving Carlyle in the near future.

The filing divulged that Carlyle is highly profitable. In the first six months of this year, the company’s profits were $770 million. The company earned about $1 billion in 2010.

It also has been profitable for global investors in Carlyle’s 84 funds, which own all or part of 270 companies and properties around the world, including Asian forests, a Brazilian lingerie firm, rental car company Hertz, Nielsen and rest stops along Connecticut highways.

Since its inception in 1987, the firm has generated a 31 percent annual return for those investors, which include pension funds, insurance companies, sovereign wealth funds and wealthy individuals, firm officials have said.

“They are very successful,” Blaydon said.

The private equity business is built on buying companies, often with large amounts of debt, and then selling them in three to six years for big profits. The industry standard is for the private equity firm to charge up to a 2 percent management fee on the total amount of the funds and take a fifth of any profits it earns.

Carlyle management fees were $483 million in the first six months of 2011 compared with $402 million for the same period in 2010. Performance fees were $1.2 billion for the first six months of 2011 compared with $111 million in 2009, evidence that Carlyle has enjoyed a very successful year so far despite the gloomy economy.

The filing does not say where and when the company will sell its shares, or for what price. It is also unclear how much stock in the firm will be in the initial offering.

JP Morgan Chase, Citigroup and Credit Suisse will lead the initial public offering.

Carlyle’s sale of shares to the public has been anticipated for years and follows two other major private equity rivals, the Blackstone Group and Kohlberg Kravis & Roberts.

Aside from its founders, the firm is owned by Mubadala, the investment arm for the emirate of Abu Dhabi, with 9 percent, and California’s pension system, which owns 5 percent. Carlyle’s 100 partners own the remainder.