AMID THE WELL-HEELED RETIREES WHO PLAY GOLF and walk the beach in Carmel-by-the-Sea, California, economist William Sharpe is hard at work. Professor emeritus at Stanford University and winner of a 1990 Nobel Prize, the 78-year-old Sharpe is deeply immersed in the study of “retirement economics.” He’s tackling the knotty question of how growing ranks of retirees — especially the gray brigade of baby boomers — can live off their savings as they reach ages unimaginable to earlier generations.

Sharpe’s work is crucial to financial firms racing to serve investors who hope somehow to fund their golden years. From 1970 to 2007 the retired lifetime of an American male increased by 34 percent, according to a paper published by Amy Kessler, head of longevity reinsurance at Prudential Retirement, in Longevity Risk Management for Institutional Investors, an Institutional Investor journal. American males now live an average of 17.5 years once they hit age 65, compared with 13 in 1970. Women survive almost 20 more years, up from 15 in 1970.

“I’m trying to understand the properties of different schemes for investing and spending and annuitizing in retirement,” says Sharpe in a phone interview from his home. “And there are zillions of them. Every part of the industry, from insurers to mutual funds to advisers, are all coming up with magic formulas, magic investment strategies. But there are no simple answers. It’s a difficult and complex problem.”

Sharpe and his compatriots studying retirement economics begin with some sobering math: U.S. corporate pension plans face a $689 billion deficit, while public plans in the U.S. are underfunded by about $4.4 trillion, according to a 2012 study by Harvard University’s John F. Kennedy School of Government. Individuals saving on their own fall woefully short of what they need as well — some $4.3 trillion short, according to an estimate by the Washington-based Employee Benefit Research Institute. EBRI’s 2012 Retirement Security Projection Model analyzed retirement income for baby boomers born between 1948 and 1964 (though the generation is usually defined as the 1946–’64 age cohort), and Gen Xers, born between 1964 and 1974. In an analysis for Institutional Investor, EBRI research director Jack VanDerhei concluded that an increase in longevity of just two years would push up his estimate of the shortfall to almost $5 trillion.