| Title:
|
Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion (English) |
| Author:
|
González-Hernández, Juan |
| Author:
|
López-Martínez, Raquiel R. |
| Author:
|
Minjárez-Sosa, J. Adolfo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
5 |
| Year:
|
2009 |
| Pages:
|
737-754 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process $\left\{ x_{t}\right\} $ and the discount process $\left\{ \alpha _{t}\right\} $ evolve according to the coupled difference equations $x_{t+1}=F(x_{t},\alpha _{t},a_{t},\xi _{t}),$ $ \alpha _{t+1}=G(\alpha _{t},\eta _{t})$ where the state and discount disturbance processes $\{\xi _{t}\}$ and $\{\eta _{t}\}$ are sequences of i.i.d. random variables with densities $\rho ^{\xi }$ and $\rho ^{\eta }$ respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities $\rho ^{\xi }$ and $\rho ^{\eta }$ are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy. (English) |
| Keyword:
|
discounted cost |
| Keyword:
|
random rate |
| Keyword:
|
stochastic systems |
| Keyword:
|
approximation algorithms |
| Keyword:
|
density estimation |
| MSC:
|
90C40 |
| MSC:
|
93C55 |
| MSC:
|
93E10 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 1190.93105 |
| idMR:
|
MR2599109 |
| . |
| Date available:
|
2010-06-02T19:11:43Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140040 |
| . |
| Reference:
|
[1] H. Berument, Z. Kilinc, and U. Ozlale: The effects of different inflation risk premiums on interest rate spreads.Physica A 333 (2004), 317–324. MR 2100223 |
| Reference:
|
[2] L. Devroye and L. Györfi: Nonparametric Density Estimation the $L_{1}$ View.Wiley, New York 1985. MR 0780746 |
| Reference:
|
[3] E. B. Dynkin and A. A. Yushkevich: Controlled Markov Processes.Springer–Verlag, New York 1979. MR 0554083 |
| Reference:
|
[4]
: .A. Gil and A. Luis: Modelling the U. S. interest rate in terms of I(d) statistical model. Quart. Rev. Economics and Finance 44 (2004), 475–486. |
| Reference:
|
[5] R. Hasminskii and I. Ibragimov: On density estimation in the view of Kolmogorov’s ideas in approximation theory.Ann. Statist. 18 (1990), 999–1010. MR 1062695 |
| Reference:
|
[6] J. González-Hernández, R. R. López-Martínez, and R. Pérez-Hernández: Markov control processes with randomized discounted cost in Borel space.Math. Meth. Oper. Res. 65 (2007), 27–44. |
| Reference:
|
[7] S. Haberman and J. Sung: Optimal pension funding dynamics over infinite control horizon when stochastic rates of return are stationary.Insurance Math. Econom. 36 (2005), 103–116. MR 2122668 |
| Reference:
|
[8] O. Hernández-Lerma: Adaptive Markov Control Processes.Springer–Verlag, New York 1989. MR 0995463 |
| Reference:
|
[9] O. Hernández-Lerma and J. B. Lasserre: Discrete-Time Markov Control Processes: Basic Optimality Criteria.Springer–Verlag, New York 1996. MR 1363487 |
| Reference:
|
[10] O. Hernández-Lerma and J. B. Lasserre: Further Topics on Discrete-Time Markov Control Processes.Springer–Verlag, New York 1999. MR 1697198 |
| Reference:
|
[11] O. Hernández-Lerma and W. Runggaldier: Monotone approximations for convex stochastic control problems.J. Math. Syst., Estimation, and Control 4 (1994), 99–140. MR 1298550 |
| Reference:
|
[12] P. Lee and D. B. Rosenfield: When to refinance a mortgage: a dynamic programming approach.European J. Oper. Res. 166 (2005), 266–277. |
| Reference:
|
[13] R. G. Newell and W. A. Pizer: Discounting the distant future: how much do uncertain rates increase valuation? J.Environmental Economic and Management 46 (2003), 52–71. |
| Reference:
|
[14] B. Sack and V. Wieland: Interest-rate smooothing and optimal monetary policy: A review of recent empirical evidence.J. Econom. Business 52 (2000), 205–228. |
| Reference:
|
[15] M. Schäl: Conditions for optimality and for the limit of n-stage optimal policies to be optimal.Z. Wahrsch. Verw. Gerb. 32 (1975), 179–196. MR 0378841 |
| Reference:
|
[16] M. Schäl: Estimation and control in discounted stochastic dynamic programming.Stochastics 20 (1987), 51–71. MR 0875814 |
| Reference:
|
[17] N. L. Stockey and R. E. Lucas, Jr.: Recursive Methods in Economic Dynamics.Harvard University Press, Cambridge, MA 1989. MR 1105087 |
| . |
