Messrs. Gluckstern and Palm had met teaching English in Tehran, Iran, as twentysomethings in the 1970s. Mr. Gluckstern went on to become superintendent of schools in Telluride, Colo. After getting an M.B.A., he joined Lehman Brothers as an investment banker, later falling into insurance after striking up a conversation with an insurance executive while strolling with his baby daughter in a New York City park.

That executive recommended him for a job with a Berkshire Hathaway unit specializing in reinsurance, a huge but obscure sector that insures insurers against big losses on the policies they sell to individuals and companies. There, he reunited with Mr. Palm, who also had relatively little insurance experience.

"I could barely spell the word reinsurance," Mr. Gluckstern told a reporter years later. "But in some businesses, there's a value in not knowing anything because there is no conventional wisdom."

Reinsurers at the time were on a roller coaster, gaining in calm years, losing spectacularly in bad. So the unconventional pair -- they sported blue jeans and eschewed the buttoned-down insurance world's annual conventions -- started writing low-risk multiyear policies that offered accounting and tax advantages. As the concept caught on, they branched out on their own, raising an astounding $290 million from an array of prominent industry players for their new company, Centre Reinsurance Holdings Ltd.

They set up shop in Bermuda, already an insurance Mecca 700 miles off the coast of the Carolinas thanks to low taxes and hands-off regulation. They considered calling their product "limited insurance," but rejected that as shifty-sounding, later settling on "finite risk insurance."

"When you get down to it, every large corporation must pay its own losses. Who else will?" Centre Re's 1991 annual report said. "No insurer can repeatedly pay losses in excess of premiums; nor should any corporation repeatedly pay premiums in excess of losses. While finite risk insurance cannot eliminate losses, a well-structured program can minimize their financial impact by reducing transactions costs and allowing a corporation to provide for losses over a period of years in a stable, budgeted manner."

Centre Re sold billions of dollars of so-called finite in a few years, almost exclusively to other insurers. Competitors flocked to Bermuda to sell such nontraditional insurance products, increasingly focusing on noninsurance companies. With liability insurance then at sky-high prices, many companies were opting to pay for catastrophes out of their cash flow, which provided no tax advantage. Here was a chance to draw them back into the insurance world.

"Centre Re was the envy of everybody," says Robert Newhouse, then an executive with insurance brokerage firm Marsh & McLennan Cos. "Everybody felt they had to get finite into their stable."

Then came the backlash: Old-school insurers questioned finite's accounting advantage, with some anonymously mailing excerpts of questionable policies to the Financial Accounting Standards Board in Norwalk, Conn. Naysayers complained that some policies involved little or no risk on the part of the insurers, because the premiums were almost guaranteed to cover all claims.

Following intense debate, the board in December 1992 ruled that to qualify for insurance accounting, there needed to be a "reasonable possibility" that the insurer "may realize a significant loss." Otherwise, buyers had to treat the contracts like loans. But what was "reasonable" and "significant"? Nobody ever gave a definitive ruling, but a generally accepted liberal interpretation -- at least a 10% chance of a 10% loss -- helped sustain the finite fad.

By then, Messrs. Gluckstern and Palm were moving on: Mr. Gluckstern left Centre Re in 1993 to launch a hedge fund in New York; he later bought part of the New York Islanders hockey team. Mr. Palm also left Centre Re and become a philanthropist before dying of AIDS in 1998 at age 47.

They left behind a booming finite industry, populated by expatriates from the New York and Philadelphia insurance hubs as well as locals. Insurance brokers got into the game, too. Marsh & McLennan dubbed their Marsh Alternative Risk Financing brokers with a name that today may seem a bit too apt: "financial engineers."

Among those who joined the game was AIG's Robert E. Omahne, who had been churning out cookie-cutter policies for corporate directors and officers. "It was boring," he recalls. Finite "was a chance to be creative." Mr. Omahne went on to help AIG become a big player in the field, selling policies to major companies. He says he always made sure that AIG took on sufficient risk, but he says others at AIG were less careful.

"The culture at AIG was to make budgets," Mr. Omahne says. "Everybody seized on finite as a way to make their numbers. Anything having to do with finite sprung up all over the company." He says he asked Mr. Greenberg to stop other AIG units from selling finite insurance because he worried whether their policies would past regulatory muster, to no avail. AIG and Mr. Greenberg declined to comment.

In 1998, Mr. Omahne says cellphone distributor Brightpoint Inc. of Plainfield, Ind., approached him seeking a policy to absorb part of a $29 million loss in England because it was much higher than the $13 million to $18 million loss it earlier had disclosed. "I told them to take a walk," he says. AIG and Brightpoint declined to comment.

But other AIG underwriters, from its so-called Loss Mitigation Unit, agreed to help Brightpoint -- a decision they likely came to regret. The unit's marketing literature said that "companies can secure coverage for existing claims in order to contain or avoid any negative impact on financial statements [to] provide comfort to Wall Street."

In a deal that authorities later said amounted to nothing more than a risk-free fiscal round trip, Brightpoint paid AIG $15 million in future "premiums" in return for $11.9 million in insurance proceeds to offset the trading loss, allowing it to avoid disclosing the full loss.

Mr. Omahne joined rival ACE Ltd. in 2000 as president of ACE Financial Solutions, a new unit focused on nontraditional insurance. He took several AIG employees with him and promised to make his new employer a "formidable player in what many of us see as a reinvention, rather than an evolution, of the insurance industry." In late 2002, he wrote in a trade magazine that ACE saw strong demand for "finite-risk solutions" from energy, health-care, financial and pharmaceutical companies.

That turned out to be finite's peak. The fever pitch was cooling, as some insurers realized they hadn't done such a good job limiting their risk. Several big finite-specialty firms stopped writing new policies in 2002 amid mounting losses.

By then, regulators were looking at the industry more closely. Authorities in Virginia and Australia started examining Berkshire Hathaway policies suspected of helping disguise the deteriorating condition of now-insolvent insurers in their jurisdictions. Those probes continue, and Berkshire says it is cooperating with them.

Authorities also caught wind of the Brightpoint deal. Without admitting or denying wrongdoing, AIG ended up paying fines totaling $136 million to settle criminal and civil earnings-manipulation inquiries into Brightpoint and another suspect deal involving PNC Financial Services Group Inc. Under the pact, an independent monitor now is combing through AIG's books in search of other questionable deals.

Today, investigators from the SEC, the Justice Department and the New York Attorney General's office are combing through dozens of contracts by multiple insurers, including ACE and Chubb Corp. All say they are cooperating. In recent weeks, two insurance companies -- RenaissanceRe Holdings Ltd. and Mbia Corp. -- have announced earnings restatements to correct the accounting treatment they used for reinsurance policies they bought.

At AIG, state and federal regulators are focused on a finite-insurance contract it bought from Berkshire Hathaway's General Re Corp. four years ago. That inquiry, following several unrelated regulatory inquiries involving AIG, is what prompted its board to move against Mr. Greenberg, who has run the company since 1967, long before anyone had ever heard of finite insurance.

Write to Ianthe Jeanne Dugan at ianthe.dugan@wsj.com¹¹ and Theo Francis at theo.francis@wsj.com¹²