They have their work cut out for them. Older millennials, born in the early 1980s, entered adulthood just as the dotcom bubble burst and terrorists took down the World Trade Center. Just a few years later the housing market crashed, and the country plunged into the Great Recession. Even the youngest millennials, born at the turn of the century, are entering a job market that is still recovering.

Despite the financial challenges they face, millennials themselves still feel pretty optimistic: Recent surveys have found a significant majority believe they will be at least as well off as their parents, and probably better off over the long run.

If you've read recent headlines, you might think so. But don't write them off just yet.

One report last year pegged the unemployment rate among millennials at more than 15 percent, and another estimated millennials made up about 40 percent of all unemployed Americans—or about 4.6 million.

The competitive job market has prompted millennials to pursue degrees in larger numbers – they are the most educated of any generation. But those degrees have come at a steep price. The Project on Student Debt found the average debt load carried by last year's class of four-year nonprofit college grads was $28,400, roughly 50 percent more than a decade ago. And the degrees (even advanced ones) have proven no guarantee for a well-paying job.

"Millennials are facing strong headwinds in securing satisfactory careers," said Peter Miller, certified financial planner and president of Zoe Wealth Management in Charlotte, N.C. They're also entering the workforce at a time when pensions are fading away, and unlike their parents, they're wary of depending on Social Security payments to cover expenses later in life, he said.

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But that may prove to be a blessing. Their pessimism has prompted many to start saving earlier and to participate more in their retirement savings accounts than baby boomers did at their age. According to a Transamerica Center fore Retirement Studies report, 70 percent of millennials are already saving for retirement in a company-sponsored 401(k) or a similar plan or outside the workplace.

True, unemployment and underemployment can affect their access to retirement accounts like 401(k)s and, of course, their ability to save much. Yet millennials remain optimistic about their ability to save.

Seventy-two percent of millennials are confident they will be able to save enough to create the lifestyle they want in the future, and 68 percent expect their standard of living before retirement to be better than their parents, according to a recent Wells Fargo survey.

And advisors say millennials have reason to be upbeat about their long-term prospects. For one, time is on their side. They've also got an awareness of the importance of saving early for retirement. In the Wells Fargo survey, 80 percent said the Great Recession had taught them they need to save now to be prepared for economic problems down the road, and 55 percent were already saving.

"They do have the opportunity to be very different from their parents' generation," said Miller, adding that millennials are young enough to accumulate savings and benefit from years of compounding.

He also noted that millennials have been less inclined to take on consumer debt, perhaps because many already carry the burden of student loan debt. "Their parents' generation saw debt, and sometimes massive, crippling debt, as a way of life," Miller said.

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But millennials seem warier of credit-card debt than older peers. A Bankrate.com survey last year found 63 percent of them don't have credit cards, compared with just 35 percent of those over 30 years old.

Another advantage millennials have is technology. Not only do banks have more mobile services, but there are dozens of apps available to help them manage their money and stay on top of savings and investments. Many—like BudgetSimple, Mint.com and Spendee—are free and can be accessed easily from a mobile phone.

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"There are more opportunities for millennials to be better prepared financially [than their parents]," said Marguerita Cheng, certified financial planner and CEO of Blue Ocean Global Wealth in Maryland. "If they use their intellectual capital and use the time they have to improve their financial capital then they can get it right."