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      Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets

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      Author
      Pınar, M. Ç.
      Date
      2013
      Source Title
      Optimization Letters
      Print ISSN
      1862-4472
      Electronic ISSN
      1862-4480
      Volume
      7
      Issue
      1
      Pages
      63 - 78
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a "no good-deal assumption" defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by a multi-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software.
      Keywords
      American options
      Mixed-integer second-order cone optimization
      American options
      Computational results
      Conic optimization
      Contingent claims
      Financial market
      Finite-state
      Incomplete financial markets
      Incomplete markets
      Mixed-integer
      Multi-period
      No arbitrage
      Scenario tree
      Second order cone
      Second-order cone programming
      Sharpe ratios
      Commerce
      Decision trees
      Finance
      Optimization
      Risk perception
      Integer programming
      Permalink
      http://hdl.handle.net/11693/21130
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s11590-011-0394-z
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      • Department of Industrial Engineering 677
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