The Effect of Improvements in Health and Longevity on Optimal Retirement and Saving

We develop a life-cycle model of optimal retirement and savings behavior under complete markets where retirement is caused by worsening health in old age. Our model explains the long-run decline in the age of retirement as an income level effect. We show that improvements in health and longevity tend to increase the desired retirement age, though less than proportionately, while, contrary to conventional views, reducing savings rates. The retirement age is not simply proportional to healthy lifespan because compound interest creates a wealth effect when lifespan increases, leading to more leisure (early retirement) and higher consumption (lower savings).Health, longevity, savings, retirement

The Effect of Improvements in Health and Longevity on Optimal Retirement and Saving

We develop a life-cycle model of optimal retirement and savings behavior under complete markets where retirement is caused by worsening health in old age. Our model explains the long-run decline in the age of retirement as an income level effect. We show that improvements in health and longevity tend to increase the desired retirement age, though less than proportionately, while, contrary to conventional views, reducing savings rates. The retirement age is not simply proportional to healthy life span because compound interest creates a wealth effect when lifespan increases, leading to more leisure (early retirement) and higher consumption (lower savings).

Mortality transition and differential incentives for early retirement.

Many studies specify human mortality patterns parametrically, with a parameter change affecting mortality rates at different ages simultaneously. Motivated by the stylized fact that a mortality decline affects primarily younger people in the early phase of mortalitytransition but mainly older people in the later phase, we study how a mortality change at an arbitrary age affects optimal retirement age. Using the Volterra derivative for a functional, we show that mortality reductions at older ages delay retirement unambiguously, but that mortality reductions at younger ages may lead to earlierretirement due to a substantial increase in the individualʼs expected lifetime human wealth.incentive for early retirement; lifetime human wealth effect; years-to-consume effect; mortality decline;

Revisiting a Theorem of L.A. Shepp on Optimal Stopping

Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with martingales. Without martingale theory one could hardly prove our guess to be correct.Comment: 5 page

Exercising Control When Confronted by a (Brownian) Spider

We consider the Brownian "spider," a construct introduced in \cite{Dubins} and in \cite{Pitman}. In this note, the author proves the "spider" bounds by using the dynamic programming strategy of guessing the optimal reward function and subsequently establishing its optimality by proving its excessiveness.Comment: Final version. Operations Research Letters (2016); 8 pages, 1 figur

Mortality Change, the Uncertainty Effect, and Retirement

We examine the role of changing mortality in explaining the rise of retirement over the course of the 20th century. We construct a model in which individuals make labor/leisure choices over their lifetimes subject to uncertainty about their date of death. In an environment in which mortality is high, an individual who saved up for retirement would face a high risk of dying before he could enjoy his planned leisure. In this case, the optimal plan is for people to work until they die. As mortality falls, however, it becomes optimal to plan, and save for, retirement. We simulate our model using actual changes in the US life table over the last century, and show that this 'uncertainty effect' of declining mortality would have more than outweighed the 'horizon effect' by which rising life expectancy would have led to later retirement. One of our key results is that continuous changes in mortality can lead to discontinuous changes in retirement behavior.

Demographic Change, Social Security Systems, and Savings

In theory, improvements in healthy life expectancy should generate increases in the average age of retirement, with little effect on savings rates. In many countries, however, retirement incentives in social security programs prevent retirement ages from keeping pace with changes in life expectancy, leading to an increased need for life-cycle savings. Analyzing a cross-country panel of macroeconomic data, we find that increased longevity raises aggregate savings rates in countries with universal pension coverage and retirement incentives, though the effect disappears in countries with pay-as-you-go systems and high replacement rates