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An optimal stopping problem for fragmentation processes

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  • Kyprianou, Andreas E.
  • Pardo, Juan Carlos

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.

Suggested Citation

  • Kyprianou, Andreas E. & Pardo, Juan Carlos, 2012. "An optimal stopping problem for fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1210-1225.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1210-1225
    DOI: 10.1016/j.spa.2011.12.009
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    References listed on IDEAS

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    1. Maulik, Krishanu & Zwart, Bert, 2006. "Tail asymptotics for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 156-177, February.
    2. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
    3. Jagers, Peter, 1989. "General branching processes as Markov fields," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 183-212, August.
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