Prudential's shares fell on their debut on the Hong Kong and Singapore stock markets after they were caught up in a slide in global equity prices.
There are also concerns about Prudential's planned £24.6bn ($35.5bn) takeover of AIG's Asia arm, AIA.
Prudential wants to attract Asian investors for its £14.5bn rights issue, which will help fund the AIA deal.
But there is some opposition to the deal, as investors have questioned whether Prudential is paying too much.
Prudential chairman Harvey McGrath said he was confident of shareholder approval for the takeover.
"I think the vast majority are very comfortable with the transaction," said Mr McGrath, who was in Hong Kong for the share opening.
In Hong Kong, Prudential shares were slightly down from their opening price of $59.70 Hong Kong dollars at HK$58.90.
In Singapore, they were also down from the opening price of 7.72 Singapore dollars at SG$7.41.
The insurer needs a 75% shareholder vote on 7 June to get the AIA deal approved.
While some investors believe AIA could be a good business, there are questions about whether Prudential is paying the right price.
There was further pressure on Tuesday with a report in the Financial Times saying that AIA's chief executive Mark Wilson planned to quit the business in the event of a takeover.
He was reported to have told colleagues that a joint Prudential-AIA business could not work.
Asian investors have until 4 June to decide whether they want to participate in the rights issue.
Prudential is keen to attract more Asian shareholders ahead of the 7 June meeting, because of the opposition already being voiced by some UK shareholders.
Prudential is currently the number two life insurer in Asia, following AIA, which has about 30 million customers in the region.
The combined firm "New Prudential" would be a dominant player in Asia, where the population is becoming wealthy enough to afford insurance.