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A consumption-investment problem modelled as a discounted Markov decision process. (English) Zbl 1241.93053
Summary: In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions which guarantee that a policy is optimal for the problem if and only if it satisfies the EE. The problem is exemplified in two particular cases: for a logarithmic utility and for a Cobb-Douglas utility. In both cases, explicit formulas for the optimal policy and the optimal value function are supplied.

MSC:
93E12 Identification in stochastic control theory
62M02 Markov processes: hypothesis testing
91B42 Consumer behavior, demand theory
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