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On income fluctuations and capital gains
Authors:Marilda A de Oliveira Sotomayor
Institution:Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rua Marquês de São Vicente, 225-CEP 22.453, Rio de Janeiro, Brasil
Abstract:We consider the infinite time horizon problem of asymptotically maximizing the expected accumulated discounted utility in a one-good production economy. The available capital in a given period is given by the production of the previous period plus a random variable. The product of the discount and interest factors is either (1) greater than or (2) equal to one. Under (1) the optimal policy exists under certain conditions and always under (2). The optimal capital sequence almost surely goes to infinity. Under (1) with conditions on the utility one almost surely reaches a capital level above which the sequence is increasing.
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