DALLAS — Airlines can't control the economy, but by limiting the number of seats for sale they are pushing up fares and earning their biggest profits in three years.

Delta, US Airways and the parent of American Airlines all posted higher-than-expected earnings for the peak summer travel season. They were helped by rapid growth in international traffic and a budding recovery in corporate travel. Delta and US Airways gave upbeat outlooks for the upcoming holidays.

Investors rewarded the companies by driving airline stocks sharply higher.

Delta shares climbed nearly 11 percent to $12.97, American parent AMR Corp. soared more than 12 percent to $7.32, and US Airways Group Inc. rose nearly 9 percent to $10.97 in afternoon trading.

US Airways CEO Doug Parker said the airlines are reaping big profits despite a sluggish economy and relatively high fuel expenses. He said they've cut costs, raised money from fees and grown smarter about pricing tickets.

"The airline industry is the industry recording record or near-record profits while the rest of U.S. industry is not," Parker told analysts and reporters. "That hasn't happened before."

Most of the other big U.S. airlines are scheduled to report results today. Analysts expect the eight top carriers to post a combined adjusted profit of $2.4 billion, which would be their best performance since the third quarter of 2007.

When fuel prices soared and then the global economy slowed, airlines grounded planes and cut flights. They've restored some of those cuts this year, but not all of them, leaving fewer available seats than existed in 2008.

That's helped the airlines boost fares. American said passenger yield, or the average fare per mile, rose nearly 11 percent compared with last summer.

The biggest airlines — the ones that fly all over the world — are also benefiting now that international travel is growing much more rapidly than traffic within the U.S.

Delta Air Lines Inc. increased its presence in Asia when it bought Northwest Airlines, and it has added a dozen new nonstop trans-Pacific routes since 2008. Those moves paid huge dividends this summer.