Stock prices surged worldwide yesterday to give a stormy October a sunny finish, as the Dow Jones industrial average closed 55.20 points higher at 1993.53.

For the week, the Dow average of 30 blue-chip stocks climbed 42.80 points, recovering from Monday's staggering 156.83-point loss.

Broad-based buying on all major U.S. stock exchanges yesterday followed an exceptionally strong buying spree on the Tokyo Stock Exchange, where the Nikkei index closed up 3.3 percent and posted its third biggest daily point gain ever.

The dramatic change in sentiment in Tokyo was significant because it followed a major selloff on Thursday. When Wall Street posted big gains Thursday, disregarding Tokyo's setback, worldwide investor sentiment appeared to turn more positive.

"The underlying thing that moves the market is psychology," said Don Hayes, director of research at Wheat, First Securities in Richmond.

"The psychology today was hope for the future. {But} unless there is some good startling news to change the psychology quite a bit, we are due for some drudgery," he said.

The New York Stock Exchange and other major markets announced after the close of trading yesterday that they plan to gradually increase their hours next week.

The normal 9:30 a.m.-to-4 p.m. session was shortened by two hours this week.

Next week, the NYSE said it will close at 2:30 p.m. on Monday through Wednesday and at 3 p.m. on Thursday and Friday.

NYSE Chairman John J. Phelan Jr., who said that shortening trading hours had given securities firms more time to process heavy trading volume, predicted that trading hours would move back to normal by Monday, Nov. 9, "barring any unforeseen events in the market."

Phelan said that the markets are "beginning to stabilize," although trading volume remained exceptionally heavy.

Trading on the NYSE yesterday totaled 303.3 million shares, nearly double a normal day before Oct. 19.

Advancing stocks outpaced declining shares on the NYSE by more than 7 to 1 yesterday.

Market analysts said one of the bullish forces driving stocks was the sense that U.S. policymakers have decided to concentrate on keeping interest rates down, which should boost the domestic economy.

At the same time, those policymakers appear to have relaxed their emphasis on supporting the value of the dollar relative to other currencies.

Federal Reserve Governor Wayne Angell, appearing before a House banking subcommittee, said he considered the Fed's injection of cash into the economy as a temporary measure to deal with the market situation, the Dow Jones news service reported.

Angell also said Fed actions to control how much money is in the economy would be based only on domestic considerations.

The falling dollar has caused concern that the Fed might tighten credit to raise interest rates so that foreigners continue to invest in this country.

Earlier in the week big declines in the value of the dollar made some investors nervous -- especially foreigners, who feared the declining currency would undermine the value of U.S. investments.

"You have had a switch in opinion as to how people are perceiving the decline in the dollar. All of a sudden it seems to have been viewed as a positive," said Merrill Lynch analyst Walter Murphy. "I'm not sure why, but that is the reaction I am getting. It will probably allow interest rates to go still lower."

"We have seen a change in investor attitude in the last 48 hours," said Peter Canelo, chief investment strategist at Bear, Stearns. "The fundamental reason is we are going to defend the economy and not the dollar, so we don't have to worry about interest rates now. This is really a plus for earnings of export companies."

Meanwhile, the stock market appeared to be unaffected by Great Britain's decision Thursday to go forward with a controversial $12.4 billion sale of stock in British Petroleum Co. over the objections of major U.S. investment firms that face large losses in the deal.

The underwriters, including four leading Wall Street firms that are attempting to sell the BP stock in this country, had warned that if the offering went forward it might undermine investor confidence in the London and U.S. stock markets.

Facing heavy international lobbying and strong domestic political pressures, Prime Minister Margaret Thatcher announced that the offering of the British government's 31.5 percent stake in BP would begin as scheduled yesterday. But in a compromise, the British government said it would take steps if necessary to prevent the price of BP shares from falling below Thursday's closing price.

The four U.S. underwriters involved -- Goldman, Sachs & Co., Morgan Stanley & Co., Salomon Inc. and Shearson Lehman Bros. -- committed to buy BP stock for U.S. distribution at a fixed price before the worldwide financial panic that struck international markets on Oct. 19. The firms began selling their shares yesterday, but Wall Street sources said the offer was heavily undersubscribed in both nations.

The new BP issue was the most heavily traded stock on the NYSE yesterday as 13,180,400 shares changed hands. The stock closed at $17.25 per American depository receipt, each of which represents 12 BP shares.

That price accounts for only the first of three installment payments investors must make before next spring.

When all payments are accounted for, yesterday's closing price is still above the floor at which the British government said Thursday it would buy back shares.

Wall Street sources said that at the floor set by the British government, Morgan, Salomon, and Shearson face pretax losses of $96 million each in the deal, with Goldman facing a slightly larger loss because it is the lead manager of the offering. If the price of BP shares holds above the floor, the losses will be smaller, the sources said.

The heavy losses faced by four of Wall Street's best-known firms reflect a growing willingness by these and other investment houses to risk large amounts of their own capital in huge stock and takeover deals. The firms' readiness to take large risks with their capital has grown dramatically in recent years as the bull stock market rushed ahead and takeover activity boomed.

Among the ways in which Wall Street firms risked capital in the months before the stock market collapse was by making so-called bridge loans in corporate takeovers. In a bridge loan, an investment firm uses its own money to provide short-term financing for an acquisition.

Because the stock market's fall has quelled takeover activity and thrown uncertainty into stock prices and financings, some outstanding bridge loans may create further losses for the big investment firms. Salomon, for example, has $600 million in bridge loans outstanding, representing the firm's share of financing in at least four pending takeover deals, a spokesman said.

British Petroleum was followed on the NYSE active list yesterday by Tenneco, up 1 3/8 to 44 3/8; AT&T, up 1/2 to 29 7/8, and Union Carbide, up 2 3/8 to 21 1/2.

The American Stock Exchange index closed up 18.06 at 260.36, while the index of over-the-counter stocks closed at 323.29, up 16.24.

"Nerves are steadier and generally speaking it is difficult to forecast what the market is going to do now," said Bonnie Wachtel, vice president of Washington-based Wachtel & Co. Inc. "We are getting out of that mode of rebound and that makes it difficult to predict which way things are going."

Said Shearson Lehman Bros. chief economist Allen Sinai: "Calm it is not. It is still a very fragile market environment."