Аннотация:
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the weighted likelihood ratios hit stochastic boundaries depending on the current observations. The proof is based on the reduction of the initial problems into appropriate three-dimensional optimal stopping problems and the analysis of the associated parabolic-type free-boundary problems. We provide closed-form estimates for the value functions and the boundaries, under certain nontrivial relations between the coefficients of the observable diffusion.
The hospitality and financial support from the Alexander von Humboldt Foundation through the fellowship for experienced researchers is gratefully acknowledged.
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Статья
Язык публикации: английский
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Эта публикация цитируется в следующих 19 статьяx:
Pavel V. Gapeev, Yavor I. Stoev, “Quickest Change-point Detection Problems for Multidimensional Wiener Processes”, Methodol Comput Appl Probab, 27:1 (2025)
Erik Ekström, Alessandro Milazzo, “A detection problem with a monotone observation rate”, Stochastic Processes and their Applications, 172 (2024), 104337
Pavel V. Gapeev, Monique Jeanblanc, “On the Construction of Conditional Probability Densities in the Brownian and Compound Poisson Filtrations”, ESAIM: PS, 28 (2024), 62
Neha Deopa, Daniele Rinaldo, “Quickest Detection of Ecological Regimes for Natural Resource Management”, Environ Resource Econ, 2024
Kristoffer Glover, Goran Peskir, “Quickest Detection Problems for Ornstein–Uhlenbeck Processes”, Mathematics of OR, 2023
Bruno Buonaguidi, “Finite Horizon Sequential Detection with Exponential Penalty for the Delay”, J Optim Theory Appl, 198:1 (2023), 224
Philip Ernst, Hongwei Mei, “Exact Optimal Stopping for Multidimensional Linear Switching Diffusions”, Mathematics of OR, 48:3 (2023), 1589
Erhan Bayraktar, Erik Ekström, Jia Guo, “Disorder detection with costly observations”, J. Appl. Probab., 59:2 (2022), 338
B. Buonaguidi, “The disorder problem for diffusion processes with the ϵ-linear and expected total miss criteria”, Statistics & Probability Letters, 189 (2022), 109548
Bruno Buonaguidi, “On the dimension reduction in the quickest detection problem for diffusion processes with exponential penalty for the delay”, Electron. Commun. Probab., 26:none (2021)
Pavel V. Gapeev, Yavor I. Stoev, “On some functionals of the first passage times in jump models of stochastic volatility”, Stochastic Analysis and Applications, 38:1 (2020), 149
Liang Cai, “Quickest detection of an accumulated state-dependent change point”, Sequential Analysis, 39:2 (2020), 230
Thomas Kruse, Philipp Strack, “An Inverse Optimal Stopping Problem for Diffusion Processes”, Mathematics of OR, 44:2 (2019), 423
Pavel V. Gapeev, Hessah Al Motairi, “Perpetual American Defaultable Options in Models with Random Dividends and Partial Information”, Risks, 6:4 (2018), 127
PAVEL V. GAPEEV, OLIVER BROCKHAUS, MATHIEU DUBOIS, “ON SOME FUNCTIONALS OF THE FIRST PASSAGE TIMES IN MODELS WITH SWITCHING STOCHASTIC VOLATILITY”, Int. J. Theor. Appl. Finan., 21:01 (2018), 1850001
P. Johnson, J. Moriarty, G. Peskir, “Detecting changes in real-time data: a user's guide to optimal detection”, Phil. Trans. R. Soc. A., 375:2100 (2017), 20160298
Thomas Kruse, Philipp Strack, “An Inverse Optimal Stopping Problem for Diffusion Processes”, SSRN Journal, 2017
Pavel V. Gapeev, “Bayesian Switching Multiple Disorder Problems”, Mathematics of OR, 41:3 (2016), 1108
B. Buonaguidi, P. Muliere, “On the martingale and free-boundary approaches in sequential detection problems with exponential penalty for delay”, Stochastics, 86:6 (2014), 865
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