* Dow, S&P 500 at all-time highs; last week was best in months

U.S. stocks jumped on Monday, with the Dow and S&P 500 advancing to all-time highs as Apple Inc surged on a distribution deal with China Mobile and lifted the technology sector.

Volume is expected to be thin this week, with many market participants out for the Christmas holiday. Equity markets will close early on Tuesday and will be closed all of Wednesday. The light volume could amplify market volatility.

Tech titan Apple said on Sunday it had signed a long-awaited agreement with China Mobile Ltd to sell iPhones through the world’s biggest network of mobile phone users, a deal that could add billions of dollars to its revenue.

The deal “clearly invites a new demographic and an entire new generation of users that are going to be introduced to these Apple products,” said Todd Schoenberger, managing partner at LandColt Capital in New York. “Just off the deal alone with China Mobile, that can equate to a 10 percent upside on Apple’s stock.”

Shares of Apple shot up 3.4 percent to $567.88. The stock’s massive market capitalization helped lift both the S&P 500 and the Nasdaq. U.S.-listed shares of China Mobile rose 2 percent to $52.67.

The Dow Jones industrial average was up 83.10 points, or 0.51 percent, at 16,304.24. The Standard & Poor’s 500 Index was up 10.19 points, or 0.56 percent, at 1,828.51. The Nasdaq Composite Index was up 38.47 points, or 0.94 percent, at 4,143.21.

Facebook Inc, which soared 5.3 percent to $58.02, also helped bolster the Nasdaq and the S&P 500. Monday market the social networking company’s first day of trading as an S&P 500 component.

Both the Dow and the S&P 500 were at all-time highs, extending sharp gains from last week, the strongest for major indexes in months.

The rally was fueled by strong economic data and the U.S. Federal Reserve’s decision to begin trimming its stimulus program next month, which removed a major source of uncertainty for the market. The Fed also said its key interest rate would stay at rock bottom longer than previously promised.

The S&P 500 has soared about 28 percent this year, thanks largely to the Fed’s stimulus, and is on track for its best year since 1997.

In the latest economic data, a survey showed that consumer sentiment rose to its strongest in five months in December as Americans’ outlook on the economy and job prospects improved. However, the figure was slightly below expectations for the Thomson Reuters/University of Michigan’s final December reading on consumer sentiment.

November personal income rose 0.2 percent while spending rose 0.5 percent, according to a Commerce Department report. Analysts expected both to have risen 0.5 percent. The market wasn’t affected by the data.

Retail stocks will be in focus in the final shopping days leading up to Christmas. In a sign that this season may be a difficult one for the sector, U.S. consumers shopped less during the final weekend before Christmas despite deeper discounts, according to analytics firm RetailNext.

“We’re a little nervous about the holiday season,” said Oliver Pursche, president of Gary Goldberg Financial Services, which is based in Suffern, New York. “Sales have been strong, but there has been significant discounting going on, especially in the middle-end section. That could hurt the bottom line.”

Target Corp may see particular trouble in the wake of a massive data breach. The Wall Street Journal reported that the retailer suffered reduced customer traffic over the weekend, which is one of the busiest of the year. Target’s stock fell 1.1 percent to $61.81.