Pricing American perpetual warrants by linear programming

Robert J. Vanderbei, Mustafa Ç Pinar

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A warrant is an option that entitles the holder to purchase shares of a common stock at some prespecified price during a specified interval. The problem of pricing a perpetual warrant (with no specified interval) of the American type (that can be exercised any time) is one of the earliest contingent claim pricing problems in mathematical economics. The problem was first solved by Samuelson and McKean in 1965 under the assumption of a geometric Brownian motion of the stock price process. It is a well-documented exercise in stochastic processes and continuous-time finance curricula. The present paper offers a solution to this time-honored problem from an optimization point of view using linear programming duality under a simple random walk assumption for the stock price process, thus enabling a classroom exposition of the problem in graduate courses on linear programming without assuming a background in stochastic processes.

Original languageEnglish (US)
Pages (from-to)767-782
Number of pages16
JournalSIAM Review
Issue number4
StatePublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


  • American option
  • Duality
  • Dynamic programming
  • Harmonic functions
  • Linear programming
  • Perpetual warrant
  • Pricing
  • Second-order difference equations


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