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Computational Algorithms for Vertical Complementarity Arising in Finance


  • Berç Rustem

    () (Imperial College)

  • Tetsuya Noguchi

    () (Imperial College)

  • Michael Selby

    () (Imperial College)


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.

Suggested Citation

  • Berç Rustem & Tetsuya Noguchi & Michael Selby, 1999. "Computational Algorithms for Vertical Complementarity Arising in Finance," Computing in Economics and Finance 1999 931, Society for Computational Economics.
  • 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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