In a speech, White dismissed the claims of 'Flash Boys' author Michael Lewis that the market is rigged, insisting that it is "not fundamentally broken, let alone rigged" and warned that the SEC should not "roll back the technology clock or prohibit algorithmic trading".

However, she did argue that steps need to be looked at to ensure that the new high-tech trading world works for investors, not against them.

Among the proposals being worked on is a move to bring unregistered active proprietary traders under the SEC's remit, subjecting them to the watchdog's rules as dealers. In addition, an exception from Finra membership requirements for dealers that trade in off-exchange venues could be scrapped.

Meanwhile, White is asking exchanges and Finra to consider including a time stamp in the consolidated data feeds that indicates when a trading venue, for example, processed the display of an order or execution of a trade.

White says that she is "wary of prescriptive regulation that attempts to identify an optimal trading speed," but is open to things such as batch auctions or other mechanisms that minimise speed advantages.

The SEC chair also signalled her discomfort with the lack of transparency surrounding dark pools, which now account for around 35% of US trading volume. While ATSs have to disclose some details of their operations with the SEC, these are not made public.

White wants to increase the amount of information it gets from these venues and is even considering making it public to help investors track what their brokers are doing.

Kenneth Bentsen, CEO, Sifma, welcomed White's "thoughtful remarks," adding: "Investor confidence in the fairness of the equity markets is essential to an efficient financial system that drives economic growth in our country."

Finra also applauded the speech, adding: "Finra supports expanding its ATS trading volume disclosure system to include all off-exchange venues, thereby shedding more light on what are now opaque areas of trading to investors.