| Title:
|
Stability estimating in optimal stopping problem (English) |
| Author:
|
Zaitseva, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
400-415 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space $X$. It is supposed that an unknown transition probability $p(\cdot |x)$, $x\in X$, is approximated by the transition probability $\widetilde{p}(\cdot |x)$, $x\in X$, and the stopping rule $\widetilde{\tau }_*$, optimal for $\widetilde{p}$, is applied to the process governed by $p$. We found an upper bound for the difference between the total expected cost, resulting when applying $\widetilde{\tau }_*$, and the minimal total expected cost. The bound given is a constant times $\displaystyle \sup \nolimits _{x\in X}\Vert p(\cdot |x)-\widetilde{p}(\cdot |x)\Vert $, where $\Vert \cdot \Vert $ is the total variation norm. (English) |
| Keyword:
|
discrete-time Markov process |
| Keyword:
|
optimal stopping rule |
| Keyword:
|
stability index |
| Keyword:
|
total variation metric |
| Keyword:
|
contractive operator |
| Keyword:
|
optimal asset selling |
| MSC:
|
60G40 |
| MSC:
|
60J10 |
| idZBL:
|
Zbl 1154.60326 |
| idMR:
|
MR2436040 |
| . |
| Date available:
|
2009-09-24T20:35:40Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135859 |
| . |
| Reference:
|
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