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Computational Algorithms for Vertical Complementarity Arising in Finance

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  • Ber� Rustem

    ()
    (Imperial College)

  • Tetsuya Noguchi

    ()
    (Imperial College)

  • Michael Selby

    ()
    (Imperial College)

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    Abstract

    We consider efficient computational algorithms for vertical complementarity problems. Vertical complementarity represents the equilibrium relationship among functions such that min (F1(x),...,Fm(x))=0 . This form is more general than the ordinary complementarity relationship, min (x, F(x))=0 . We consider an application in finance in terms of an option-hedging problem under transaction costs formulated as a singular stochastic control problem. This is expressed as a quasi-variational inequality. It is fully nonlinear and non-differentiable and belongs to a class of multi-dimensional free boundary problems equivalent to a vertical complementarity problem. In order to solve the quasi-variational inequality, alternative formulations are investigated. In addition, efficient numerical schemes are considered to provide a numerical solution.

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    Bibliographic Info

    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 931.

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    Date of creation: 01 Mar 1999
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    Handle: RePEc:sce:scecf9:931

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    Cited by:
    1. Tetsuya Noguchi & Berc Rustem, 2002. "An algorithm for the quasivariational inequality arising in option pricing with transaction costs II," Computing in Economics and Finance 2002 379, Society for Computational Economics.

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