Additionally, the Allstate Corporation, which is 80 percent owned by Sears, reported surprisingly positive results, reflecting lower-than-expected losses for the insurer in automobile and catastrophe coverage.

The Allstate Corporation said yesterday that earnings fell 22 percent in the first quarter, pulled down by insurance claims filed as a result of the severe winter.

But much of the volume came from two big active issues - Hanson P.L.C. and the initial public offering of the Allstate Corporation.

While the city of Chicago houses most of the major brokerage firms, many insurance companies are in the city or suburbs, such as Allstate Corporation.

The Allstate Corporation said yesterday that its net income rose 47.2 percent in the second quarter, primarily because of a strong increase in the collection of premiums.

The Lucent offering would surpass the $2.4 billion initial stock sale of the Allstate Corporation by Sears, Roebuck & Company in June 1993.

The Allstate Corporation is the second-largest personal lines insurer in the United States (behind State Farm) and the largest that is publicly held.

Encompass Insurance Company is a subsidiary of The Allstate Corporation.

The Allstate Corporation entered the stock-market history books yesterday, but not everyone was cheering.

If Sears sells all the additional shares it has in reserve, the Allstate Corporation would have 450 million shares outstanding after the offerings.