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      Pricing American perpetual warrants by linear programming

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      Author
      Vanderbei, R.J.
      Pinar, M. Ç.
      Date
      2009
      Source Title
      SIAM Review
      Print ISSN
      0036-1445
      Electronic ISSN
      1095-7200
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      51
      Issue
      4
      Pages
      767 - 782
      Language
      English
      Type
      Article
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      91
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      Abstract
      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.
      Keywords
      Pricing
      Perpetual warrant
      American option
      Linear programming, duality
      Lynamic programming
      Harmonic functions
      Second-order difference equations
      Permalink
      http://hdl.handle.net/11693/22502
      Published Version (Please cite this version)
      http://dx.doi.org/10.1137/080728366
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      • Department of Industrial Engineering 677
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