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


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.


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


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

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

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