Shares of Priceline.com Inc., the most valuable online travel agency, rose to the highest price in more than a decade on Monday, after Morgan Stanley set a target price exceeding $1,000 for the shares.

Priceline stock, which has more than quadrupled since the end of 2009, climbed 3.9 percent to $888.63 at the close in New York, the highest price since May 1999.

As Priceline gains market share globally, the economic environment improves and more bookings move online, investors will pay a higher price for the company’s earnings, Scott Devitt, an analyst at Morgan Stanley, wrote in a research report Monday. He upgraded the stock to overweight from equal weight and raised his price estimate by 33 percent to $1,010.

Aided by the European Booking.com unit, reservations outside the U.S. are bolstering Priceline’s results even as competition with rivals such as Expedia Inc. intensifies. The Norwalk, Connecticut-based company in May reported first-quarter profit that topped estimates, with the international business accounting for 85 percent of bookings.

“Priceline has gained market share in the European online travel agency space amidst heightened competition from Expedia,” Devitt said. “Booking.com will maintain its dominant competitive position due to its strong value proposition to hotels and customers.”

The increased price target makes Morgan Stanley more bullish than any of the 23 estimates tracked by Bloomberg. The next highest price is $975 from Ascendiant Capital Markets. Devitt predicted the stock will trade at 20 to 21 times earnings, up from a current multiple of about 17.

Morgan Stanley, based in New York, has missed the recent rally in Priceline shares. Devitt downgraded the stock to equal weight in January. He maintained that rating after quarterly results on May 9, lifting the stock price target the following day to $760 from $740, while reiterating concern about “margin compression.”

Since the close of trading on May 9, Priceline shares have jumped 20 percent.