89
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

From Disorder Detection to Optimal Stopping and Mathematical Finance

&
Pages 112-124 | Received 27 Mar 2009, Accepted 01 Jun 2009, Published online: 17 May 2010

REFERENCES

  • Baron , M. and Tartakovsky , A. G. ( 2006 ). Asymptotic Optimality of Change-Point Detection Schemes in General Continuous-Time Models , Sequential Analysis 25 : 257 – 296 (Invited Paper in Memory of Milton Sobel) .
  • Baurdoux , E. J. and Kyprianov , A. E. ( 2008 ). The Shepp-Shiryaev Stochastic Game Driven by Spectrally Negative Levy Process , Teoriya Veroyatnostej i ee Primeneniya 53 : 588 – 609 .
  • Beibel , M. ( 1996 ). A Note on Ritov's Bayes Approach to the Minimax Property of the Cusum Procedure , Annals of Statistics 24 : 1804 – 1812 .
  • Burnaev , E. V. , Feinberg , E. A. , and Shiryaev , A. N. ( 2008 ). On Asymptotic Optimality of the Second Order in the Quickest Detection of the Drift for Brownian Motion , Teoriya Veroyatnostej i ee Primeneniya 53 : 557 – 575 (in Russian).
  • Feinberg , E. A. and Shiryaev , A. N. ( 2006 ). Quickest Detection of Drift Change for Brownian Motion in Generalized Bayesian and Minimax Settings , Statistics & Decisions 24 : 445 – 470 .
  • Fuh , C. D. (2003). SPRT and CUSUM in Hidden Markov Models, Annals of Statistics 31: 942–977.
  • Fuh , C. D. ( 2004 ). Asymptotic Operating Characteristics of an Optimal Change Point Detection in Hidden Markov Models , Annals of Statistics 32 : 2305 – 2339 .
  • Jacod , J. and Shiryaev , A. N. ( 1987, 2003 ) . Limit Theorems for Stochastic Processes , Berlin : Springer-Verlag .
  • Lai , T. L. ( 1998 ). Information Bounds and Quick Detection of Parameter Changes in Stochastic Systems , IEEE Transactions on Information Theory 44 : 2917 – 2929 .
  • Liptser , R. Sh. and Shiryaev , A. N. ( 1986, 1989 ) . Theory of Martingales , Dordrecht : Kluwer .
  • Liptser , R. Sh. and Shiryaev , A. N. ( 2001 ). Statistics of Random Processes I, II , Berlin : Springer-Verlag .
  • Lorden , G. ( 1971 ). Procedures for Reacting to a Change in Distribution , Annals of Mathematical Statistics 42 : 1897 – 1908 .
  • Mei , Y. ( 2008 ). Is Average Run Length to False Alarm Always an Informative Criterion? Sequential Analysis 27 : 354 – 376 .
  • Moustakides , G. V. ( 1986 ). Optimal Stopping Times for Detecting Changes in Distributions , Annals of Statistics 14 : 1379 – 1387 .
  • Moustakides , G. V. ( 2004 ). Optimality of the CUSUM Procedure in Continuous Time , Annals of Statistics 32 : 302 – 315 .
  • Moustakides , G. V. , Polunchenko , A. S. , and Tartakovsky , A. G. ( 2009 ). Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions , Communications in Statistics: Theory and Methods 38 : 3225 – 3239 .
  • Moustakides , G. V. , Polunchenko , A. S. , and Tartakovsky , A. G. ( 2010 ). A Numerical Approach to Comparative Efficiency Analysis of Quickest Change-Point Detection Procedures, Statistica Sinica, in press.
  • Page , E. S. ( 1954 ). Continuous Inspection Schemes , Biometrika 41 : 100 – 115 .
  • Peskir , G. ( 2008 ). Optimal Stopping Games and Nash Equilibrium , Teoriya veroyatnostej i ee Primeneniya 53 : 623 – 638 .
  • Peskir , G. and Shiryaev , A. N. ( 2000 ). Sequential Testing Problems for Poisson Processes , Annals of Statistics 28 : 837 – 859 .
  • Peskir , G. and Shiryaev , A. N. ( 2002 ). Solving the Poisson Disorder Problem , Advances in Finance and Stochastics . pp. 295 – 312 , Berlin : Springer-Verlag .
  • Peskir , G. and Shiryaev , A. N. ( 2006 ). Optimal Stopping and Free Boundary Problems , Lectures in Mathematics , ETH Zürich : Birkhäuser .
  • Pollak , M. ( 1985 ). Optimal Detection of a Change in Distribution , Annals of Statistics 13 : 206 – 227 .
  • Pollak , M. and Siegmund , D. ( 1985 ). A Diffusion Process and its Applications to Detecting a Change in the Drift of Brownian Motion , Biometrika 72 : 267 – 280 .
  • Pollak , M. and Tartakovsky , A. G. ( 2008 ). Asymptotic Exponentiality of the Distribution of First Exit Times for a Class of Markov Processes with Applications to Quickest Change Detection , Teoriya Veroyatnostej i ee Primeneniya 52 : 500 – 515 .
  • Pollak , M. and Tartakovsky , A. G. ( 2009 ). Optimality Properties of the Shiryaev–Roberts Procedure , Statistica Sinica 19 : 1729 – 1739 .
  • Polunchenko , A. S. and Tartakovsky , A. G. ( 2010 ). On Optimality of the Shiryaev–Roberts Procedure for Detecting Changes in Distributions, Annals of Statistics, in press.
  • Ritov , Y. ( 1990 ). Decision Theoretic Optimality of the Cusum Procedure , Annals of Statistics 18 : 1466 – 1469 .
  • Roberts , S. W. ( 1966 ). A Comparison of Some Control Chart Procedures , Technometrics 8 : 411 – 430 .
  • Shepp , L. and Shiryaev , A. N. ( 1993 ). The Russian Option: Reduced Regret , Annals of Applied Probability 3 : 631 – 640 .
  • Shiryaev , A. N. ( 1961a ). The Problem of the Most Rapid Detection of a Disturbance in a Stationary Process , Soviet Mathematics—Doklady 2 : 795 – 799 .
  • Shiryaev , A. N. (1961b). The Detection of Spontaneous Effects, Soviet Mathematics—Doklady 2: 740–743.
  • Shiryaev , A. N. ( 1963 ). On Optimum Methods in Quickest Detection Problems , Theory of Probability and Its Applications 8 : 22 – 46 .
  • Shiryaev , A. N. ( 1969 ). Statistical Sequential Analysis: Optimal Stopping Rules , Moscow : Nauka , 1969 (in Russian) .
  • Shiryaev , A. N. ( 1978 ). Optimal Stopping Rules , New York : Springer-Verlag .
  • Shiryaev , A. N. ( 1996 ). Minimax Optimality of the Method of Cumulative Sum (Cusum) in the Case of Continuous Time , Russian Mathematical Surveys 51 : 750 – 751 .
  • Shiryaev , A. N. ( 2002 ). Quickest Detection Problems in the Technical Analysis of the Financial Data , in Mathematical Finance-Bachelier Congress 2000 . H. Geman , D. Madan , S. R. Pliska , and T. Vorst , eds., pp. 487 – 521 , Berlin : Springer Finance (Selected Papers from the First World Congress of the Bachelier Finance Society, Paris, June 29–July 1, 2000).
  • Srivastava , M. S. and Wu , Y. ( 1993 ). Comparison of EWMA, CUSUM and Shiryayev–Roberts Procedures for Detecting a Shift in the Mean , Annals of Statistics 21 : 645 – 670 .
  • Tartakovsky , A. G. ( 2005 ). Asymptotic Performance of a Multichart CUSUM Test Under False Alarm Probability Constraint , in Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05), December 12–15, 2005 , pp. 320 – 325 , Seville, Spain, Omnipress CD-ROM, ISBN 0-7803-9568-9.
  • Tartakovsky , A. G. ( 2008 ). Discussion on “Is Average Run Length to False Alarm Always an Informative Criterion?” by Yajun Mei , Sequential Analysis 27 : 396 – 405 .
  • Tartakovsky , A. G. and Veeravalli , V. V. ( 2004 ). Change-Point Detection in Multichannel and Distributed Systems with Applications , in Applications of Sequential Methodologies , N. Mukhopadhyay , S. Datta and S. Chattopadhyay , eds., pp. 339 – 370 , New York : Marcel Dekker .
  • Tartakovsky , A. G. and Veeravalli , V. V. ( 2005 ). General Asymptotic Bayesian Theory of Quickest Change Detection , Theory of Probability and Its Applications 49 : 458 – 497 .
  • Recommended by Nitis Mukhopadhyay

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.