On the optimal exercise boundaries of swing put options

Tiziano De Angelis, Yerkin Kitapbayev

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We use probabilistic methods to characterise time-dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications, we consider a payoff of immediate stopping of "put" type, and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries, which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally, we provide a formula for the value function of the problem.

Original languageBritish English
Pages (from-to)252-274
Number of pages23
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 2018


  • American put option
  • Free-boundary problems
  • Optimal multiple stopping
  • Swing options


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