The problem of declining cognition is especially acute among women. They tend to live longer than men, and old age is a major risk factor for developing Alzheimer's disease. Largely because of their longevity, women account for almost two-thirds of Americans with the disease, according to the Alzheimer's Association.
Men don't get off scot-free: a study of nearly 2,000 Americans aged 70 to 89 found that 16 percent of them had some form of mild cognitive impairment, and the rate was higher for men than for women.
Still, with men being at least six years older than their female partners in nearly 1 in 5 couples, "men who do have reductions in cognitive capacity end up very often with a caregiver who can watch over them and their finances," said Laibson.
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Adding to women's challenges, they tend to accumulate less in retirement savings, thanks to time out of the workforce and the wage gap, and have generally lower levels of financial literacy and confidence. Just 20 percent of women feel very prepared to meet their long-term financial goals, a figure that has remained largely unchanged for a decade, and only a third of women believe they are in good shape when it comes to retirement savings, according to a study by Prudential.
Read MoreWhy there is a gender gap in retirement savings
And women are particularly vulnerable to elder financial abuse—they're almost twice as likely to be victimized as men, according to one study.