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      Sharpe-ratio pricing and hedging of contingent claims in incomplete markets by convex programming

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      Author(s)
      Pınar, M. Ç.
      Date
      2008-08
      Source Title
      Automatica
      Print ISSN
      0005-1098
      Electronic ISSN
      1873-2836
      Publisher
      Elsevier
      Volume
      44
      Issue
      8
      Pages
      2063 - 2073
      Language
      English
      Type
      Article
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      Abstract
      We analyze the problem of pricing and hedging contingent claims in a financial market described by a multi-period, discrete-time, finite-state scenario tree using an arbitrage-adjusted Sharpe-ratio criterion. We show that the writer’s and buyer’s pricing problems are formulated as conic convex optimization problems which allow to pass to dual problems over martingale measures and yield tighter pricing intervals compared to the interval induced by the usual no-arbitrage price bounds. An extension allowing proportional transaction costs is also given. Numerical experiments using S&P 500 options are given to demonstrate the practical applicability of the pricing scheme.
      Keywords
      Contingent Claim
      Pricing
      Hedging
      Sharpe Ratio
      Martingales
      Transaction Costs
      Convex Programming
      Permalink
      http://hdl.handle.net/11693/11636
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.automatica.2007.11.006
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