Benefiting from the surging stock market, the brokerage business last year reported record revenues of $23.2 billion and after-tax profits of $1.7 billion--a 44 percent jump over 1981, the industry's leading trade association said today.

Despite the rosy 1982 picture, the research department of the Securities Industry Association warned that expenses are rising at a rate staggering enough to raise questions about the industry's profitability during less prosperous times.

Over the three-year period ending with 1982, the annual compound growth rate for total expenses was reported at almost 26 percent, a figure that "flabbergasted" Jeffrey M. Schaefer, the SIA senior vice president and director of research. Revenues over the same period rose 27.4 percent.

Significantly, occupancy and equipment costs rose by 26 percent for the industry, raising serious questions about the viability of New York City as a headquarters, staff and communications center for increasingly automated brokerage transactions.

While much of American industry suffered in 1982, the securities business did not. While nationwide sales fell by 5.7 percent, revenues in the brokerage business jumped by 17 percent. And, while the Fortune 500's profitability fell by 27 percent, the securities industry's profits jumped by 43 percent.

Schaefer said the dramatic surge in industry expenses was particularly surprising in light of the fact that "traditionally, the business has been thought of as a fixed-cost" field.

"Costs are no longer fixed in the securities business," Schaefer said. "Costs are relentlessly going up."

Data processing and communications expenses rose by a rate of almost 31 percent, registered representative compensation by 29.1 percent, promotional costs by 28.7 percent, and regulatory fees and expenses by 28 percent.

These figures, reflecting trends like the dramatic expansion of industry marketing and advertising, reflect both the success of the industry and the new competition traditional brokerage houses face from discounters, banks, savings and loans and others. In addition, the data processing costs, in large part, reflect the fact that financial instititutions are spending enormous amounts of money in updating data processing systems to keep pace with evolving technologies.

"These expense levels are of concern because the volatility of revenues, characteristic of this industry, shows no signs of relenting," the SIA research department said in an annual report. "Revenue growth could slow down which would adversely affect the industry."

Although Schaefer had no specific suggestions for brokerage executives, he said in an interview that he would "look everywhere" to cut operational expenses.

The industry's volatility is obvious, the SIA official said, noting that profitability for the 1982 first quarter--well before the August beginning of the stock market's boom--was reported at a 5.4 percent return on investment. During that quarter, 43 percent of New York Stock Exchange firms lost money.

But for the fourth quarter of 1982, the return on investment figure jumped to 42.8 percent. The 1982 fourth quarter produced 54 percent of the industry's profits, the SIA said.