For centuries Lloyd's of London has dominated the high-risk, big-preminum insurance business.

From the bizarre to the brand-new, Lloyd's underwriters had a reputation for being willing to take on almost anything from Jimmy Durante's nose to supertankers and satellites.

About half the $4 billion in premium insurance that syndicates at Lloyd's take in every year come from the United States. That money flies to London, in large part, because U.S. insurance companies have not had the forum to put together the complex, innovative deal.

The United States will take its first stab at capturing some of that insurance business that goes to London because it has nowhere else to go when the New York Insurance Exchange Inc. opens its doors at 8:45 tomorrow morning. It will be the world's second insurance exchange.

The exchange will operate much like Lloyd's. Brokers with a premium deal to put together will talk among underwriters representing major insurance syndicates gathered under a central roof on John Street in downtown Manhattan.

New York State will restrict the types of insurance that can be written on the exchange: no personal lines, for example, nor any premiums under $100,000. But brokers will be able to negotiate policies for their business clients without the rate-setting interference of the New York State Insurance Department.

Insurance companies and brokers long have complained that it is too difficult to put together complicated insurance deals in the United States beacuse of tight regulations most states put on underwriting.

The business is equally complicated because no one insurer wants to take 100 percent of big-risk policies, and negotiating with different companies -- often scattered across the country -- was difficult.

As at Lloyd's, a broker at the new exchange will be able to present his insurance needs to one underwriter after another until he can sign on enough risk-takers to cover his client's interests.

Donald E. Reutershan, president of the New York Insurance Exchange, admits that the new body is not about to put an immediate dent in Lloyd's $4 billion in underwriting premiums -- nor the $4 billion more in big-business risk premiums that other London-based underwriting syndricates take in.

"But what might change is the amount of growth that gets directed to Lloyd's," the former Sentry Group insurance executive said.

New York insurance sources said the exchange hopes to capture between $40 million and $50 million in high-risk premiums its first year.

Several other states are thinking of taking on Lloyd's market as well. A similar exchange is planned in Chicago, and Florida and California also may get in on the act.

Reutershan said exchange will have 16 to 17 syndicates -- each with a minimum capitalization of $3.55 million -- when it opens, and he hopes to have 30 to 40 syndicates operating within a few months.

The syndicates will be represented by underwriters who have the authority to take a certain piece of the insurance risk (and premium) for the members of that syndicate.

At Lloyd's all members of a syndicate are persons who theoretically at least have unlimited liability for claims against them. If claims against the syndicate exceed the capital a member has in the syndicate, the individual member must come up with more funds commensrate to the percentage of the syndicate he or she owns.

At the New York exchange, the syndicate structure may be either corporate (where liability is limited) or personal. So far, all the syndicates are corporate, Reutershan said.

The Continental Insurance Group heads a syndicate called Maidenlane (a well-know Wall Street area concourse), and the Insurance Company of North America heads up the 1792 syndicate.

Other syndicates will be headed by companies such as Alliance, Crum & Forster and General Reinsurance.

The exchange will write three types of insurance: direct insurance on risks that are located outside the United States, reinsurance (insurance one insurance company buys from another to spread out the risk) and customers that have been turned down by at least three insurance companies belonging to what is called New York's insurance free-trade zone.

Since 1978, companies belonging to the zone have been able to take on large business risks without the approval of the state insurance department.

Besides the 16 or 17 syndicates that will be members of the exchange, at least 40 brokerage firms will be direct members and many others associate members.

Direct broker members can take on business from other brokers as well as directly from a client. Associate brokers may negotiate only with underwriters on behalf of a client company.

It will be some time before the exchange will be able to handle the biggest of the large-sized risks negotiated in London. Although many of the syndicates ave increased their capital base from the monimum $3.55 million and although officials hope the number of syndicates will grow from 16 to 40 by the end of the year, there are nearly 400 syndicates at Lloyd's.

Furthermore, a large chunk of Lloyd's business is maritime -- it was founded nearly three centuries ago at a coffee shop in London to insure ships and did nothing else until 1877 -- and at present the New York exchange will not insure maritime risks.

Nevertheless,the former colonies' challenge to the London market comes at a time when Lloyd's faces probably its fiercest financial challenge of the century and its severest internal squabbling in its history.

Lloyd's losses were heavy in 1979, and several of its syndicates are threatened with bankruptcy. Many Lloyd's members contend that the exchange's internal controls on the types of insurance its members write were not stirct enough and that some risks were insured that should not have been.

Although Lloyd's itself does not write insurance anymore than the New York Stock Exchange trades stocks, it does restrict the behavior of its members.

"Greed got the better of them in several cases," contends one London broker who is a member of Lloyd's.

The biggest case in point is the risks Lloyd's syndicates underwrote for big computer-leasing comapnies, mainly American.

Lloyd's permitted underwriters to guarantee computer-leasing companies against finacial losses they might incur if customers were to cancel their leases. Lloyd's wrote the coverage from 1973 unitl 1978.

Exchange syndicates may now be liable for as much as $300 million in claims from computer-leasing companies who had customers opt out of their rental agreements when Interational Business Machines Corp. introduced a new computer.