Optimal Consumption with a Stochastic Income Stream - Miller, Bruce L. (Econometrica, 1974)
An infinite horizon consumption model is considered where the labor part of income is random. An upper bound on optimal consumption is obtained by considering the expected value of the optimal return function in the deterministic labor income case. This upper bound on consumption is easily shown to be lower than the value of optimal consumption in the case where the random labor income is replaced by its mean.