Aging Population, Retirement, and Risk Taking: Reply
回应了原论文中定理1的技术错误，通过增加一个条件（两种方式可选）确保长期内股票优于债券，并基于常见偏好和实证证据支持该结论，对退休储蓄者具有指导意义。
In theorem 1 given in my paper, “Aging Population, Retirement, and Risk Taking” [Levy H (2016a) Aging population, retirement, and risk taking. Management Sci. 62(5):1415–1430.], there is indeed a technical error. Yet, adding one condition to the theorem (which can be added in two alternate ways) is sufficient to ensure the dominance of stocks over bonds in the very long run. For the commonly employed preferences, the empirical evidence conforms with the claim given in my original theorem 1, asserting that the portfolio with the higher geometric mean (stocks) dominates the other portfolio under consideration (bonds) as the investment horizon increases indefinitely. Thus, as advocated in my paper, stocks dominate bonds for investors with typical preferences who save for retirement. This paper was accepted by Karl Deither, finance.