NEW YORK, DEC. 11 -- The stock market today closed out its best week since its October collapse with a modest advance in quiet trading.

The Dow Jones average of 30 industrials rose 11.60 to 1867.04, finishing the week with a net gain of 100.30 points.

That surpassed the previous record weekly point rise of 93.43 set Aug. 10-14, when the market was nearing the end of its five-year climb.

The figure appeared less dramatic, however, from the perspective of the extraordinary volatility of the market lately. Last week the average fell 143.74 points.

Advancing issues outnumbered declines by about 5 to 4 in the daily tally of New York Stock Exchange-listed issues. Big Board volume totaled 151.68 million shares, down from 188.96 million Thursday.

On international currency markets, the dollar stumbled lower again, but light trading may have spared it even greater damage, analysts said. Gold prices were up.

The dollar moved violently on Thursday, when the government announced a record shortfall in U.S. trade during October. The news caused a massive dollar selloff that pushed the U.S. currency down to a postwar low against the Japanese yen and a near-low against the West German mark.

Today, the dollar dropped further -- to historic lows against both currencies -- but it traded in a narrow range. In late New York trading, the dollar was quoted at 128.30 yen, down from 129.06 late Thursday, and 1.6307 West German marks, down from 1.6329.

Analysts said the stock market impressed many traders with a relatively calm response to Thursday's trade deficit news.

When the market absorbs bad news without significant damage, many investors interpret it as a sign that stocks may be ripe for a rally.

A pair of economic reports issued this morning were also generally seen in a positive light.

The Labor Department said the producer price index of finished goods was unchanged in November, and the Commerce Department reported a 0.2 percent rise in retail sales for the same month.

Texaco climbed 3 7/8 to 35 7/8 and Pennzoil jumped 6 3/4 to 79 3/4 on reports that negotiators were about to make a major step toward settling the two companies' long legal battle.

American Telephone & Telegraph, which said its earnings for 1987 would be better than it had expected earlier, edged up 1/4 to 27 3/8.

Among other actively traded blue chips, Exxon gained 1 1/4 to 39 1/4; General Electric 7/8 to 43 5/8, and American Express 1/4 to 21 3/4. International Business Machines slipped 7/8 to 110 1/8.

A.H. Robins fell 1 1/2 to 14 1/4. A federal judge ruled that the company must set aside about $700 million more than Robins had proposed to pay claims relating to its Dalkon Shield contraceptive device.

Church's Fried Chicken rose 7/8 to 6 7/8. A group including members of the Bass family of Fort Worth said it had acquired an 8.2 percent stake in the company for investment.