Optimal multiple stopping and valuation of swing options

René Carmona, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


The connection between optimal stopping of random systems and the theory of the Snell envelop is well understood, and its application to the pricing of American contingent claims is well known. Motivated by the pricing of swing contracts (whose recall components can be viewed as contingent claims with multiple exercises of American type) we investigate the mathematical generalization of these results to the case of possible multiple stopping. We prove existence of the multiple exercise policies in a fairly general set-up. We then concentrate on the Black-Scholes model for which we give a constructive solution in the perpetual case, and an approximation procedure in the finite horizon case. The last two sections of the paper are devoted to numerical results. We illustrate the theoretical results of the perpetual case, and in the finite horizon case, we introduce numerical approximation algorithms based on ideas of the Malliavin calculus.

Original languageEnglish (US)
Pages (from-to)239-268
Number of pages30
JournalMathematical Finance
Issue number2
StatePublished - Apr 2008


  • Multiple American exercise
  • Optimal multiple stopping
  • Swing options

ASJC Scopus subject areas

  • Applied Mathematics
  • Economics and Econometrics
  • Accounting
  • Finance
  • Social Sciences (miscellaneous)


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