Stock prices fell during most of today's session, as small investors sold steadily while big institutional investors such as pension funds did little buying or selling at all.

The Dow Jones average of 30 industrial stocks closed at 932.25, down 15.02 points on the day. It had been as low as 928.24 at 3:30 p.m. but rallied slightly during the last 30 minutes of trading.

Analysts attributed the big one-day decline to renewed investor worries over the economy and the Reagan administration's ability to do anything to counter high interest rates and inflation in the short term.

Even cuts in the so-called broker loan rate by several major banks -- as well as a small Michigan bank's cut in its prime lending rate to 17 1/2 percent -- did little to buoy confidence.Many major banks are quoting a 19 1/2 percent prime rate for their best business customers (although many are at 20 percent), but a reduction in the rates charged brokers often precedes a cut in the prime rate.

Most analysts do not believe today's decline in stock prices signals bad things to come. Instead, they said, big investors appear to be waiting for President Reagan's economic address on Thursday.

In the past few weeks, trading volume has been light by recent standards: 44.5 million shares changed hands on the New York Stock Exchange, up from 41.2 million shares on Friday.

Without institutions buying, as they were early in the year, the "relentless selling" by the smaller investors depresses prices, according to Jerry Hinkle, chief trader for Sanford C. Bernstein & Co., a brokerage firm that deals with institutional customers.

"It's the euphoria of the post-Reagan victory being replaced by reality," Hinkle said. He noted pessimistic statements by a number of Republican leaders, including Senate Majority Leader Howard Baker of Tennessee, over the weekend as contributing to the climate on Wall Street.

Only 293 stocks closed higher in price today, while 1,320 declined.

On the American Stock Exchange, prices were down sharply, as well. The Amex index declined 11 points to 334.03, with 527 stocks falling in price and 120 stocks rising.

Oil company stocks, which were one of the major factors behind the strong stock market performance in 1980, continued their losing ways of the new year. Mobil fell 2 3/4 to 70 1/4, Standard Oil of Indiana 1/2 to 66 3/4, Shell was 1 3/8 to 46 1/8, and Standard Oil of Ohio 1 3/4 to 58 1/4.

In the government bond market, prices were off between $10 and $15 per $1,000 of face value as market participants awaited a major $8.5 billion Treasury Department financing venture this week.

Corporate bond prices declined as well, although only about half as much as Treasury securities.

The NYSE's composite index of all of its listed stock fell 1.60 to 72.67.

At the American Stock Exchange, the market value index was down 11.00 at 334.03. The NASDAQ composite index for the over-the-counter market closed at 193.09, off 4.72.