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The hedge fund titan Steven A. Cohen sat at the center of his vast trading floor on Monday, buying and selling stocks. In a sign of his enduring influence on Wall Street, he did business with major banks like Goldman Sachs and JPMorgan Chase.

Just last week, Mr. Cohen appeared relaxed courtside at Madison Square Garden while watching the New York Knicks defeat the Milwaukee Bucks in their season opener. And he will soon be closely monitoring the auctions at Sotheby’s and Christie’s, which are selling about $80 million worth of art from his vaunted collection, including two Warhol paintings and a Cy Twombly sculpture.

For the 57-year-old billionaire, it is business as usual.

But on Monday, federal prosecutors announced that Mr. Cohen’s firm, SAC Capital Advisors, had agreed to plead guilty to insider trading violations and pay a record $1.2 billion penalty, becoming the first large Wall Street firm in a generation to confess to criminal conduct. The government has also forced SAC to terminate its business of managing money for outside investors.

Insider trading at SAC was “substantial, pervasive and on a scale without precedent in the history of hedge funds,” said Preet Bharara, the United States attorney in Manhattan. His office has criminally charged eight former SAC employees; six have pleaded guilty.

Mr. Cohen’s apparent nonchalance — even as the firm bearing his initials admitted it was a criminal organization — reflects what is missing from the plea deal. After more than a decade of poring over trading records, interviewing informants and issuing grand jury subpoenas, federal authorities have not been able to build a case against SAC’s billionaire owner.

Without such a case, Mr. Cohen could still be a force on Wall Street, which has long, deep relationships with SAC. With its rapid-fire trading style, the hedge fund has been a top stock-trading client of the major banks, paying them billions of dollars in commissions. The banks have also made big profits extending loans to the fund. On Monday, they all continued to trade with SAC.

According to his friends on Wall Street, Mr. Cohen says that he has done nothing wrong and thinks the government is bent on destroying him and his firm. Mr. Cohen, who owns 100 percent of SAC, has also privately complained that he has to pay more than $1 billion out of his own pocket for the crimes of rogue employees.

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A statement issued by SAC’s senior management on Monday appeared to underscore Mr. Cohen’s frustrations, minimizing the extent of the wrongdoing and distancing Mr. Cohen from the misconduct.

“We take responsibility for the handful of men who pleaded guilty and whose conduct gave rise to SAC’s liability,” the firm said. “The tiny fraction of wrongdoers does not represent the 3,000 honest men and women who have worked at the firm during the past 21 years. SAC has never encouraged, promoted or tolerated insider trading.”

The statement, especially the last sentence, angered government officials because it contradicted SAC’s admission that it committed insider trading crimes. After prosecutors made their displeasure known to SAC, the firm issued a new statement that swapped out the last sentence and replaced it with, “Even one person crossing the line into illegal behavior is too many and we greatly regret this conduct occurred.”

The son of a retail-clothing executive and a piano teacher, Mr. Cohen grew up in Great Neck, N.Y. Today, he lives across Long Island Sound in Greenwich, Conn., in a 36,000-square-foot home with an indoor pool and a two-hole golf course.

Mr. Cohen started SAC in 1992 managing just $25 million. As the hedge fund grew, Mr. Cohen created an unorthodox structure. He sits atop a decentralized firm in which about 140 small teams each have control over hundreds of millions of dollars. The teams are all required to share their best investment ideas with Mr. Cohen, who historically has managed the largest account, worth several billion dollars.

SAC attracted ambitious, talented traders and promised them outsize pay as long as they performed. In good times, the fund’s top talent earned as much as $100 million annually. As for Mr. Cohen, he reportedly earned about $900 million a year in 2006 and 2007.

Mr. Cohen was able to pay such mammoth compensation because he charged among the highest annual fees in the hedge fund industry — 3 percent of assets and as much as 50 percent of profits. It commanded those fees after posting some of the best returns in the business — an average of 30 percent annually.

Though it branched into other strategies, SAC typically traded in stocks around market-moving events like earnings and big mergers. His traders became known for aggressively pumping sources for insights, and rumors persisted that the fund routinely crossed the line into trading on confidential corporate information.

Since early 2011, the government secured a series of guilty pleas by former SAC traders that gave legitimacy to those rumors and ultimately underpinned the indictment of the hedge fund. Prosecutors have said that one of those traders, Mathew Martoma, spoke with Mr. Cohen about his questionable trades, but he has not cooperated and awaits trial.

In recent weeks, friends say, Mr. Cohen’s spirits have been high with the hope that the settlement would resolve a major legal problem. But several challenges remain.

SAC’s plea deal does not incorporate a separate civil action the Securities and Exchange Commission brought against Mr. Cohen. The S.E.C. lawsuit has accused him of turning a blind eye to misconduct at his fund, and seeks to bar him from ever managing outside money, at SAC or elsewhere, people briefed on the case said.

Criminal authorities also continue to view Mr. Cohen and other SAC employees as targets. F.B.I. agents, the people said, are examining SAC’s trading records and seeking the cooperation of potential informants.

The investigation has exacted a significant toll on SAC. Nearly all the fund’s investors have pulled their money. But SAC was always more insulated than other hedge funds from the damaging effects of withdrawals because of the $15 billion it managed at its peak, only $6 billion was from outside investors. The balance belongs largely to Mr. Cohen.

There was speculation that an indictment of SAC might cause the fund to collapse. But the government tried to limit the potential for collateral damage on the fund’s investors and trading partners. Prosecutors did not freeze SAC’s assets and encouraged brokerage firms to continue to do business with the fund.

SAC will now most likely morph into a so-called family office, with Mr. Cohen and a staff of hundreds investing his personal wealth. And with billions at his disposal, Mr. Cohen is likely to remain a presence in the stock market.

His business associates are optimistic that he will remain a powerful force on Wall Street.

“His attitude is great and he is trying to put this behind him,” said a senior brokerage firm executive who trades with SAC. “His personal money — 9 billionish — will be plenty big.”