Shares in 21st Century Insurance Group shot up 27 percent Thursday following an offer by American International Group Inc. its majority shareholder to buy its remaining publicly held shares.

The New York insurance holding company, which owns about 62 percent of the Woodland Hills-based property and casualty insurer, offered $19.75 per share in cash, a 19 percent premium on the Wednesday closing price.

However, investors sent the shares up $4.40 to $20.99 in trading price Thursday, indicating the market expects a sweetened bid from AIG. The current bid is valued at $690 million.

If the offer is finalized, 21st Century would become a wholly owned subsidiary of the world’s largest insurance company.