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A note on Bayesian detection of change-points with an expected miss criterion

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  • Karatzas Ioannis

Abstract

A process X is observed continuously in time; it behaves like Brownian motion with drift, which changes from zero to a known constant ϑ>0 at some time τ that is not directly observable. It is important to detect this change when it happens, and we attempt to do so by selecting a stopping rule T* that minimizes the “expected miss” E|T−τ| over all stopping rules T. Assuming that τ has an exponential distribution with known parameter λ>0 and is independent of the driving Brownian motion, we show that the optimal rule T* is to declare that the change has occurred, at the first time t for which.Here, with Λ=2λ/ϑ2, the constant p* is uniquely determined in (1/2,1) by the equation.

Suggested Citation

  • Karatzas Ioannis, 2003. "A note on Bayesian detection of change-points with an expected miss criterion," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 3-14, January.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:1/2003:p:3-14:n:5
    DOI: 10.1524/stnd.21.1.3.20317
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    Cited by:

    1. Blanchet-Scalliet, Christophette & Diop, Awa & Gibson, Rajna & Talay, Denis & Tanre, Etienne, 2007. "Technical analysis compared to mathematical models based methods under parameters mis-specification," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1351-1373, May.
    2. Zhenya Liu & Yuhao Mu, 2022. "Optimal Stopping Methods for Investment Decisions: A Literature Review," IJFS, MDPI, vol. 10(4), pages 1-23, October.
    3. Erhan Bayraktar & Savas Dayanik, 2006. "Poisson Disorder Problem with Exponential Penalty for Delay," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 217-233, May.

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