| Title:
|
About stability of risk-seeking optimal stopping (English) |
| Author:
|
Montes-de-Oca, Raúl |
| Author:
|
Zaitseva, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
378-392 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space $X$. It is supposed that the transition probability $p(\cdot |x)$, $x\in X$ is approximated by the transition probability $\widetilde{p}(\cdot |x)$, $x\in X$, and that the stopping rule $\widetilde{f}_*$ , which is optimal for the process with the transition probability $\widetilde{p}$ is applied to the process with the transition probability $p$. We give an upper bound (expressed in term of the total variation distance: $\sup_{x\in X}\|p(\cdot |x)-\widetilde{p}(\cdot |x)\|)$ for an additional cost paid for using the rule $\widetilde{f}_*$ instead of the (unknown) stopping rule $f_*$ optimal for $p$. (English) |
| Keyword:
|
discrete-time Markov process |
| Keyword:
|
risk-seeking expected total cost |
| Keyword:
|
optimal stopping rule |
| Keyword:
|
stability index |
| Keyword:
|
total variation metric |
| MSC:
|
60G40 |
| MSC:
|
62L15 |
| MSC:
|
90C40 |
| idZBL:
|
Zbl 1300.60059 |
| idMR:
|
MR3245536 |
| DOI:
|
10.14736/kyb-2014-3-0378 |
| . |
| Date available:
|
2014-07-29T13:10:56Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143881 |
| . |
| Reference:
|
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| . |
