An Elementary Approach to Optimal Stopping Problems for AR(1) Sequences

被引：9

作者：

Christensen, Soeren ^{[1
]}

Irle, Albrecht ^{[1
]}

Novikov, Alexander ^{[2
]}

机构：

[1] Univ Kiel, Math Seminar, D-24098 Kiel, Germany

[2] Univ Technol Sydney, Dept Math Sci, Sydney, NSW 2007, Australia

来源：

SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS | 2011年 / 30卷 / 01期

关键词：

Autoregressive sequence; Exponential innovations; Optimal stopping; Threshold times;

D O I：

10.1080/07474946.2011.539925

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Optimal stopping problems form a class of stochastic optimization problems that has a wide range of applications in sequential statistics and mathematical finance. Here we consider a general optimal stopping problem with discounting for autoregressive processes. Our strategy for a solution consists of two steps: First we give elementary conditions to ensure that an optimal stopping time is of threshold type. Then the resulting one-dimensional problem of finding the optimal threshold is to be solved explicitly. The second step is carried out for the case of exponentially distributed innovations.

引用

页码：79 / 93

页数：15

共 10 条

[1] Alsmeyer G., 1988, Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, P183
[2] [Anonymous], 2007, Stochastics
[3] Baurdoux E. J, 2007, STOCHASTICS, V79, P183
[4] OPTIMAL STOPPING ON AUTOREGRESSIVE SCHEMES
FINSTER, M
[J]. ANNALS OF PROBABILITY, 1982, 10 (03) : 745 - 753
[5] Jacobsen M, 2006, WORKING PAPER
[6] Lerche Hans Rudolf, 2007, STOCHASTICS, V79, P275
[7] Martingales and first passage times of AR(1) sequences
Novikov, Alexander
Kordzakhia, Nino
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2008, 80 (2-3) : 197 - 210
[8] Peskir G., 2006, LEC MATH, DOI 10.1007/978-3-7643-7390-0
[9] SHIRYAEv A. N., 1978, Optimal Stopping Rules
[10] OPTIMUM CHARACTER OF THE SEQUENTIAL PROBABILITY RATIO TEST
WALD, A
WOLFOWITZ, J
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1948, 19 (03): : 326 - 339

← 1 →