The Effect of Pension on the Optimized Life Expectancy and Lifetime Utility Level

In this paper, we analyze the effect of a pension system on the life expectancy and the lifetime utility level using an optimal dynamic problem of individuals who live in continuous and finite time. Our model yields a number of intriguing results: 1) Life expectancy is not always proportional to lifetime utility. 2) The pension system can make life expectancy longer or shorter. 3) It is not always true that the pension system improves the lifetime utility level.