An income fluctuation problem
Abstract A consumer has a t period planning horizon problem, at each period, he gets additionals incomes that are i.i.d. random variables, and he must decide how much of his income will be spent in consumption, yielding some utility, and how much will be saved to maximize the total expected utility. No borrowing is allowed, and for the amounts saved no interest is paid. Using the concepts of competitive prices it is shown that as t → ∞ the corresponding limit of the consumption policy is strictly bounded above by the expected value of the random income.