We derive the ï¬rst closed-form optimal reï¬nancing rule: Reï¬nance when the current mortgage interest rate falls below the original rate by at least \(\frac{1}{ψ}\)[φ + W (− exp (−φ))]. In this formula W(.) is the Lambert W-function, ψ = \(\frac{2 (Ï +...

Many consumers make poor financial choices and older adults are particularly vulnerable to such errors. About half of the population between ages 80 and 89 either has dementia or a medical diagnosis of “cognitive impairment without dementia.†We study lifecycle patterns in financial...