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Journal of Optimization Theory and Applications

, Volume 143, Issue 2, pp 279–293 | Cite as

Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs

  • W. Li
  • S. Wang
Article

Abstract

We present a novel penalty approach to the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of European options with proportional transaction costs. We first approximate the HJB equation by a quasilinear 2nd-order partial differential equation containing two linear penalty terms with penalty parameters λ 1 and λ 2 respectively. Then, we show that there exists a unique viscosity solution to the penalized equation. Finally, we prove that, when both λ 1 and λ 2 approach infinity, the viscosity solution to the penalized equation converges to that of the corresponding original HJB equation.

Keywords

Penalty approach European option pricing Optimal control Partial differential equation Viscosity solution 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematics & StatisticsUniversity of Western AustraliaCrawleyAustralia

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