| Title:
|
A consumption-investment problem modelled as a discounted Markov decision process (English) |
| Author:
|
Cruz-Suárez, Hugo |
| Author:
|
Montes-de-Oca, Raúl |
| Author:
|
Zacarías, Gabriel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
6 |
| Year:
|
2011 |
| Pages:
|
909-929 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
discounted Markov decision processes |
| Keyword:
|
differentiable value function |
| Keyword:
|
differentiable optimal policy |
| Keyword:
|
stochastic Euler equation |
| Keyword:
|
consumption and investment problems |
| MSC:
|
62A10 |
| MSC:
|
93E12 |
| idZBL:
|
Zbl 1241.93053 |
| idMR:
|
MR2907851 |
| . |
| Date available:
|
2011-12-08T10:04:21Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141734 |
| . |
| Reference:
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