|
This article is cited in 5 scientific papers (total in 5 papers)
Two-sided disorder problem for a Brownian motion in a Bayesian setting
A. A. Muravlevab, A. N. Shiryaevca a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b International Laboratory of Quantitative Finance, National Research University Higher School of Economics, Moscow, Russia
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
Abstract:
A two-sided disorder problem for a Brownian motion in a Bayesian setting is considered. It is shown how to reduce this problem to the standard optimal stopping problem for a posterior probability process. Qualitative properties of a solution are analyzed; namely, the concavity, continuity, and the smooth-fit principle for the risk function are proved. Optimal stopping boundaries are characterized as a unique solution to some integral equation.
Received in October 2014
Citation:
A. A. Muravlev, A. N. Shiryaev, “Two-sided disorder problem for a Brownian motion in a Bayesian setting”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 211–233; Proc. Steklov Inst. Math., 287:1 (2014), 202–224
Linking options:
https://www.mathnet.ru/eng/tm3591https://doi.org/10.1134/S0371968514040128 https://www.mathnet.ru/eng/tm/v287/p211
|
|