Geodesic
A consumption-investment problem modelled as a discounted Markov decision process
Kybernetika, Tome 47 (2011) no. 6, pp. 909-929

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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.
Classification : 62A10, 93E12
Keywords: discounted Markov decision processes; differentiable value function; differentiable optimal policy; stochastic Euler equation; consumption and investment problems 
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     author = {Cruz-Su\'arez, Hugo and Montes-de-Oca, Ra\'ul and Zacar{\'\i}as, Gabriel},
     title = {A consumption-investment problem modelled as a discounted {Markov} decision process},
     journal = {Kybernetika},
     pages = {909--929},
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2011},
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     zbl = {1241.93053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a8/}
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Cruz-Suárez, Hugo; Montes-de-Oca, Raúl; Zacarías, Gabriel. A consumption-investment problem modelled as a discounted Markov decision process. Kybernetika, Tome 47 (2011) no. 6, pp. 909-929. http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a8/