Shares of Nvidia closed at their highest ever on Monday, lifting its market value to $3.39 trillion (AED 12.4 trillion) just below Apple's $3.52 trillion (AED 12.92 trillion) and above Microsoft's $3.12 trillion (AED 11.45 trillion).
Nvidia's rise sees it close to dethroning Apple Inc and become the world's most valuable company.
The return of excitement around tech, artificial intelligence and corporate earnings has set the tone in Asia, where Tokyo's Nikkei index is above 40,000 again, and is likely to propel European stock markets, too.
On Tuesday the S&P 500 soared to a record high close and the Dow Jones index scaled 43,000 points for the first time, led by chip stocks after a 2.4 per cent jump in AI darling Nvidia and a brisk start to the third-quarter earnings season.
More bank earnings are due on Tuesday. Bank of America is expected to report a fall in third-quarter profit, Goldman Sachs is expected to see higher fees from advisory and underwriting services, and Citigroup and brokerage firm Charles Schwab also report earnings.
Key for Europe among a batch of jobs and inflation data releases is the European Central Bank's survey on bank lending to the euro zone economy, which should feed into expectations for Thursday's policy review.
The ECB is set to deliver another quarter-point rate cut on Thursday, a move policymakers were reluctant to flag and traders had given less than a 25 per cent chance when the bank met a month ago.