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.
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Communicated by X.Q. Yang.
We thank Professor C.J. Goh for several constructive suggestions.
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Li, W., Wang, S. Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs. J Optim Theory Appl 143, 279–293 (2009). https://doi.org/10.1007/s10957-009-9559-7
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DOI: https://doi.org/10.1007/s10957-009-9559-7