Journal
THEORY OF PROBABILITY AND ITS APPLICATIONS
Volume 58, Issue 3, Pages 493-502Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0040585X97986734
Keywords
first hitting time; Shiryaev's inverse boundary problem; Skorokhod embedding
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Funding
- Natural Sciences and Engineering Research Council (NSERC) of Canada
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In this paper we consider a connection between the famous Skorokhod embedding problem and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion: given a probability distribution, F, find a boundary such that the first hitting time distribution is F. By randomizing the initial state of the process we show that the inverse problem becomes analytically tractable. The randomization of the initial state allows us to significantly extend the class of target distributions in the case of a linear boundary and, moreover, allows us to establish a connection with the Skorokhod embedding problem.
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