NEW YORK (Reuters) - Stocks gained and the dollar hovered near a 2-1/2-year low on Tuesday as positive coronavirus vaccine news and progress toward further U.S. fiscal stimulus and a Brexit deal encouraged investors to embrace risk. Optimism that a $1.4 trillion spending package to help the pandemic-battered U.S. economy could be imminent grew after House of Representatives Speaker Nancy Pelosi invited other top congressional leaders to meet later on Tuesday to hammer out a deal. Despite alarming COVID-19 infection and death rates across Europe and the United States, progress on vaccine rollout continued. Moderna Inc’s COVID-19 vaccine appeared set for regulatory authorization this week. The Dow Jones Industrial Average rose 345.49 points, or 1.16%, to 30,207.04, the S&P 500 gained 43.24 points, or 1.19%, to 3,690.73 and the Nasdaq Composite added 114.17 points, or 0.92%, to 12,554.21. Positive vaccine developments and hopes of greater fiscal stimulus have powered stock markets over the past few weeks, lifting shares to record highs. But the gains are prompting investors to speculate when markets will hit their peak. “I don’t think we can go much further in the short term on vaccine optimism,” said Simon Maughan, head of Trading Alpha at Liquidnet. “Profit-taking is kicking in but you can’t see it in the indices because the indices are large-tech dominated.” The number of coronavirus deaths in the United States exceeded 300,000 on Monday as the hardest-hit nation started its first vaccine inoculations, while tighter COVID-19 restrictions were imposed on London. Other countries across Europe were also set to impose new restrictions during the holiday season to limit the spread of the virus. Germany adopted a stricter lockdown on Sunday. “Much of Europe will have to weather tighter restrictions until at least early to mid-January. Q4 will be lost quarter for growth, but that should surprise no one,” said AFS analyst Arne Petimezas in Amsterdam. Europe’s broad FTSEurofirst 300 index added 0.27%, at 1,517.26. The MSCI world equity index, which tracks shares in 45 nations, rose 4.76 points or 0.76%, to 633.6. ‘FRIENDLY BACKDROP’ Last week, the United States authorized the emergency use of its first COVID-19 vaccine, developed by Pfizer and BioNTech. The vaccine has already been authorized in several countries, including Britain and Canada. “The start of vaccine approvals and distribution heightens our confidence in strong global growth in 2021. Combined with supportive policy and a fresh decline in U.S. real yields, this remains a friendly backdrop for cyclical and risky assets,” Goldman Sachs strategists said. Investors’ heightened risk appetite resulted in little demand for safe-haven currencies. The dollar index, which tracks the greenback versus a basket of six currencies, fell 0.254 points or 0.28%, to 90.457. The pound rose as markets grew more optimistic a Brexit deal would be reached ahead of the Dec. 31 deadline. The pound was up 0.8% at $1.3431. The euro was last up 0.07%, at $1.2151. Gold gained more than 1%, bolstered by expectations of more coronavirus relief aid. Spot gold prices rose $24.4901 or 1.34%, to $1,851.66 an ounce. U.S. gold futures settled up 1.3% at $1,855.30. “There is the possibility of getting stimulus passed and that is what the gold market has been waiting for,” said Jeffrey Sica, founder of Circle Squared Alternative Investments. Oil prices rose as investors focused on COVID-19 vaccine rollout, looking past the tightening of lockdowns in Europe and forecasts for a slower-than-expected recovery in fuel demand. Brent crude settled up $0.47, or 0.93%, at $50.76 a barrel. U.S. crude settled up $0.63, or up 1.34%, at $47.62 per barrel. “The crude market continues to seize upon the future outlook of the post-pandemic period, which could be as soon as next summer. A lot of us in the market sense the demand is lurking,” said John Kilduff, partner at Again Capital in New York. MSCI’s broadest index of Asia-Pacific shares outside Japan fell 1.66 points or 0.26%, to 640.29. The yen was last down 0.29%, at $103.7300.