Nelson's comments, who will take over the post from Peter Levene in October, come after several Lloyd's of London insurers in recent days gave estimates of their losses related to the devastating tsunami and earthquake which hit Japan last month.
"The challenge is to make sure that we maintain the significance and substantial improvement of underwriting standards over the last few years. That, I think, is a sine qua non for the success of Lloyd's," Nelson told Dow Jones Newswires.
Last year, Lloyd's profitability fell "because it was quite a difficult year because of claims and because of low insurance premiums and low investment returns," Nelson said.
Still, Lloyd's managed to produce a pretax profit of GBP2.195 billion, down from GBP3.868 billion a year earlier.
"That's still a good sign, but the conditions in the market remain challenging because you still have low investment returns, premiums haven't increased very much and you've already got three major catastrophes so far this year, including Japan," he said. "What we hope is that market participants are able to charge premiums--in some cases, it may be higher, sometimes it may not be--which are commensurate to the risks they're taking."
"The aim of Lloyd's is to encourage a market where the quality of underwriting, not just risk-taking, but also the quality of premiums being charged, are balanced," he said.
Among his other priorities upon being chairman, Nelson said he would like "to maintain and enhance our reputation and brand image internationally."
He said he wants to "keep on top of regulatory issues," especially the Solvency II capital regime that will be implemented in 2013.
He said he also wants to make sure that "the specialist risk facility which Lloyd's brings to the world insurance market is really used in the new emerging markets where it becomes more and more relevant."
Nelson, 63, is currently chairman of Hammerson PLC, a property investment and development company, and deputy chairman of Kingfisher PLC, Europe's biggest home-improvement retailer by sales.
Nelson said he will be leaving Kingfisher before the end of this year but will remain with Hammerson.