What action can be taken after an investor purchased stock through a corporation's initial stock offering?

The appropriate action an investor can take after purchasing stock through a corporation's initial stock offering is to move to set aside the judgment for fraud. This reflects the legal principle that if an investor believes that they were misled or defrauded during the stock offering—perhaps through materially false statements or omissions in the company's prospectus—they have the right to challenge the validity of that transaction.

In this context, if the investor can demonstrate that fraudulent information was provided that influenced their investment decision, they may seek to have the transaction annulled. This action is significant because it indicates a serious breach of trust and compliance in the securities market, which is subject to strict regulations designed to protect investors.

Other options like claiming damages due to market fluctuations or seeking compensation from the corporation's board may not be viable paths because fluctuations in market price are typically not recoverable as damages. Similarly, filing a complaint with the stock exchange, while it might raise awareness of potential issues, does not directly address the investor’s personal loss resulting from alleged fraud. Thus, the most direct legal remedy for addressing fraud in the claim is the motion to set aside the judgment.