An optimal stopping problem for fragmentation processes

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Abstract

In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to reduce it to a classical optimal stopping problem for a generalized Ornstein-Uhlenbeck process associated with Bertoin's tagged fragment. We go on to solve the latter using a classical verification technique thanks to the application of aspects of the modern theory of integrated exponential Lévy processes.
Original languageEnglish
Pages (from-to)1210-1225
Number of pages16
JournalStochastic Processes and their Applications
Volume122
Issue number4
DOIs
Publication statusPublished - Apr 2012

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