Computational Algorithms for Vertical Complementarity Arising in Finance

Berç Rustem (), Tetsuya Noguchi () and Michael Selby ()
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Berç Rustem: Imperial College
Tetsuya Noguchi: Imperial College
Michael Selby: Imperial College

No 931, Computing in Economics and Finance 1999 from Society for Computational Economics

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.

Date: 1999-03-01
New Economics Papers: this item is included in nep-fin
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