On an Optimal Stopping Problem of an Insider

Citation data:

Theory of Probability & Its Applications, ISSN: 0040-585X, Vol: 61, Issue: 1, Page: 129-133

Publication Year:
2017
Usage 11
Abstract Views 10
Link-outs 1
Citations 1
Citation Indexes 1
DOI:
10.1137/s0040585x97t98806x
Author(s):
E. Bayraktar, Zh. Zhou
Publisher(s):
Society for Industrial & Applied Mathematics (SIAM)
Tags:
Mathematics, Decision Sciences
article description
We consider the optimal stopping problem v:= supE Bposed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov Institute of Mathematics in September 2012. Here T > 0 is a fixed time horizon, (B)is the Brownian motion, ε ∈ [0,T] is a constant, and Tis the set of stopping times taking values in [ε, T ]. The solution of this problem is characterized by a path dependent reflected backward stochastic differential equation, from which the continuity of ε → vfollows. For large enough ε, we obtain an explicit expression for v, and for small ε we have lower and upper bounds. The main result of the paper is the asymptotics of vas ε ↘ 0. As a by-product, we also obtain Lévy’s modulus of continuity result in the Lsense.

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