A consumption-investment problem modelled as a discounted Markov decision process

Hugo Cruz-Suárez; Raúl Montes-de-Oca; Gabriel Zacarías

Kybernetika (2011)

  • Volume: 47, Issue: 6, page 909-929
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Cruz-Suárez, Hugo, Montes-de-Oca, Raúl, and Zacarías, Gabriel. "A consumption-investment problem modelled as a discounted Markov decision process." Kybernetika 47.6 (2011): 909-929. <http://eudml.org/doc/196815>.

@article{Cruz2011,
abstract = {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.},
author = {Cruz-Suárez, Hugo, Montes-de-Oca, Raúl, Zacarías, Gabriel},
journal = {Kybernetika},
keywords = {discounted Markov decision processes; differentiable value function; differentiable optimal policy; stochastic Euler equation; consumption and investment problems; discounted Markov decision processes; differentiable value function; differentiable optimal policy; stochastic Euler equation; consumption and investment problems},
language = {eng},
number = {6},
pages = {909-929},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A consumption-investment problem modelled as a discounted Markov decision process},
url = {http://eudml.org/doc/196815},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Cruz-Suárez, Hugo
AU - Montes-de-Oca, Raúl
AU - Zacarías, Gabriel
TI - A consumption-investment problem modelled as a discounted Markov decision process
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 6
SP - 909
EP - 929
AB - 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.
LA - eng
KW - discounted Markov decision processes; differentiable value function; differentiable optimal policy; stochastic Euler equation; consumption and investment problems; discounted Markov decision processes; differentiable value function; differentiable optimal policy; stochastic Euler equation; consumption and investment problems
UR - http://eudml.org/doc/196815
ER -

References

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