Integral equations for Rost's reversed barriers: Existence and uniqueness results

Tiziano De Angelis, Yerkin Kitapbayev

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We establish that the boundaries of the so-called Rost's reversed barrier are the unique couple of left-continuous monotonic functions solving a suitable system of nonlinear integral equations of Volterra type. Our result holds for atom-less target distributions μ of the related Skorokhod embedding problem. The integral equations we obtain here generalise the ones often arising in optimal stopping literature and our proof of the uniqueness of the solution goes beyond the existing results in the field.

Original languageBritish English
Pages (from-to)3447-3464
Number of pages18
JournalStochastic Processes and their Applications
Issue number10
StatePublished - Oct 2017


  • Free-boundary problems
  • Optimal stopping
  • Rost's reversed barriers
  • Skorokhod embedding
  • Volterra integral equations


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