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Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time Read chapter Read first chapter

2019 | OriginalPaper | Chapter

10. Some Applications to Financial Mathematics

Author : Albert N. Shiryaev

Published in: Stochastic Disorder Problems

Publisher: Springer International Publishing

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Abstract

The parameter θ is the unknown disorder time, at which the drift coefficient of the process X changes its positive valueμ1 to a negative valueμ2. Accordingly, it is natural to call X a Brownian motion with change-of-trend disorder. (Related, but different from the one treated here, is the model where the volatility (σ) undergoes a jump. Such models are known as bubble models.)Another appropriate name for the model (10.1) is that of Bachelier model with disorder (with initial condition X0 = 0; compare with [94, 95]).

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previous chapter Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models
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Shiryaev, A. N., Zhitlukhin, M. V., Ziemba, W. T. When to sell Apple and the NASDAC? Trading bubbles with a stochastic disorder model. J. Portfolio Management40 (2014), no. 2, 54–63.CrossRef
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Shiryaev, A. N., Zhitlukhin, M. V., Ziemba, W. T. Land and stock bubbles, crashes and exit strategies in Japan circa 1990 and in 2013. Quant. Finance15 (2015), no. 9, 1449–1469.MathSciNetCrossRef
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Metadata
Title
Some Applications to Financial Mathematics
Author
Albert N. Shiryaev
Copyright Year
2019
Book
Stochastic Disorder Problems

Print ISBN: 978-3-030-01525-1

Electronic ISBN: 978-3-030-01526-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-01526-8_10